Dublin Theoretical Physics Colloquium

Synge Lecture Theatre

Hamilton Building

School of Mathematics

Trinity College Dublin

Mondays

4:15 pm

### Year 2007-2008

 Month Date Speaker Title October 8 Gabriele Travaglini (Queen Mary, U.) Twistors, scattering amplitudes, and Wilson loops October 15 Romuald Janik (Jagiellonian U.) Wrapping interactions and finite size effects October 22 Lilia Anguelova (Queen Mary, U.) "O'KKLT at Finite Temperature" October 29 bank holiday November 5 Volker Schomerus (DESY) String duality in curved backgrounds November 12 Mohab Abou-Zeid (Vrije U., Brussels) Twistor Strings and Supergravity November 19 Werner Nahm (DIAS, Dublin) Finite size corrections to the thermodynamic Bethe ansatz November 26 Radu Roiban  (Penn State U.) The cusp anomalous dimension at weak and strong coupling in N=4 super-Yang-Mills theory December 3 Fernando Quevedo (Cambridge) Phenomenological and Cosmological implications of large volume string compactifications December 10 winter break December 17 winter break December 24 winter break December 31 winter break January 7 Ilka Brunner (Zurich) On defects and their fusion January 14 Margarita Garcia-Perez (Madrid) Non-perturbative physics in the Early Universe January 21 January 28 Johanna Knapp (CERN) Topological Strings, Matrix Factorizations and Deformations February 4 Richard Thomas (Imperial College) Counting curves in Calabi-Yau 3-folds February 11 Fernando Alday (Utrecht U.) Scattering Amplitudes and AdS/CFT February 18 Alexander Quintero Velez (Utrecht U.) McKay correspondence for Landau-Ginzburg models February 25 Jan Plefka (Humboldt U.) Absence of Gravitational Corrections to the Running Gauge Coupling March 3 Gregory Korchemsky (LPT, Orsay) Gluon scattering amplitudes/Wilson loops duality in N=4 super Yang-Mills theory March 10 spring break March 17 spring break March 24 spring break March 31 Wolfgang Lerche (CERN) Canceled April 7 conference April 14 Anton Gerasimov (ITEP and TCD) On Whittaker functions and related structures April 21 April 28 Peter Weisz (Munich, Max Planck Inst.) Correlation functions of the 2d non-linear O(n) sigma models May 5 holiday May 12 holiday May 19 summer break

# Titles and Abstracts of Talks

Anton Gerasimov (ITEP, Moscow and TCD)
Title:  On Whittaker functions and related structures
Abstract: For any semi-simple Lie algebra there exists  an associated
(q-deformed)  Whittaker function.  Recently proposed explicit constructions
of these functions will be  explained  and various applications to
quantum integrable systems, quantum cohomology  of flag spaces and arithmetical issues
will be discussed.

Peter Weisz (Munich, Max Planck Inst.)
Title: Correlation functions of the 2$d$ non-linear O($n$) sigma models
Abstract: Various physical quantities in non-linear O($n$) models in two
space-time dimensions can be computed at high energies using renormalized
perturbation theory because the model is asymptotically free.
But the model is also integrable, and this allows another
{\it non-perturbative approach} to solving the model
- the so called form factor bootstrap (FFB).
In this talk I will review properties of the model,
and will describe some results on correlation functions
using the FFB, which were obtained in collaboration with Janos Balog.
For example, the small $x$ behavior of structure functions (at fixed
$q^2$) is obtained. This result, which has a universal-looking form,
is partially based on intriguing factorization properties

Alexander Quintero Velez  (Utrecht U.)
Title: McKay correspondence for Landau-Ginzburg models
Abstract:
The McKay correspondence is a principle that relates the
geometry of a resolution of singularities of a quotient variety M/G and
the equivariant geometry of the group action. The classic case is
McKay's identification of the cohomology of the resolution of a Kleinian
singularity CC^2/G with the representation theory of G. In this talk, we
discuss an analogue of the McKay correspondence for Landau-Ginzburg
models. This leads naturally to a generalized notion of the McKay
correspondence as an  isomorphism of noncommutative spaces' (in
Kontsevich's sense).

Jan Plefka (Humboldt U.)
Title: Absence of Gravitational Corrections to the Running Gauge Coupling
Abstract:
The question of a modification of the running gauge coupling of (non-) abelian gauge theories by an incorporation of the quantum gravity contribution has recently attracted considerable interest. In this talk we present an involved diagrammatical calculation in the full Einstein-Yang-Mills system both in cut-off and dimensional regularization at one-loop order. It is found that all gravitational quadratic divergencies cancel in cut-off regularization and are trivially absent in dimensional regularization so that there is no alteration to asymptotic freedom at high energies. This settles the previously open question of a potential regularization scheme dependence of the one-loop beta-function traditionally computed in the background field approach. Furthermore, we show that the remaining logarithmic divergencies give rise to an effective Einstein-Yang-Mills Lagrangian with a counterterm of dimension six.

Gregory Korchemsky (LPT, Orsay)
Title: Gluon scattering amplitudes/Wilson loops duality in N=4
super Yang-Mills theory
Abstract:  We describe the proposed new duality between gluon scattering amplitudes
and light-like Wilson loops in the N=4 super-Yang-Mills theory. This
duality was established at strong coupling by Alday and Maldacena
within the AdS/CFT correspondence. We shall discuss its validity at weak
coupling. We show that the light-like Wilson loop satisfies anomalous
conformal Ward identities which unambiguously fix the form of the n=4 and
n=5 gluon amplitude but leave room for an arbitrary function of conformal
invariants for n>= 6. We report on recent two-loop calculation for the
hexagon Wilson loop and the matching 6-gluon amplitude, which indicate
that the Bern-Dixon-Smirnov conjecture is justified for n=4,5 but fails
for n >= 6.

Fernando Alday (Utrecht U.)
Title: Scattering Amplitudes and AdS/CFT
Abstract:
We describe how to compute gluon scattering amplitudes of planar
maximally super-symmetric Yang-Mills at strong coupling, using the AdS/CFT
correspondence. We explicitly show how the prescription works for the case
of four gluons. Furthermore, by considering a particular configuration
involving a large number of gluons, we test an iterative relation
conjectured to hold between scattering amplitudes at different loop orders.

Margarita Garcia-Perez
(Madrid)
Title: Non-perturbative physics in the Early Universe
Abstract: The analysis of the non-perturbative and strongly out of equilibrium
processes taking place at the end of inflation requires the use of numerical
techniques. In this talk I will focus on a scenario of low scale hybrid
inflation that can  trigger electroweak symmetry breaking.   It has been
conjectured that preheating in this set up  provides a source for phenomena
like baryogenesis or the generation of gravitational waves. I will here
describe how it can also generate a seed for long range magnetic fields in
the Universe, giving a possible solution to a long standing puzzle in
cosmology.

Johanna Knapp  (CERN)
Title: Topological Strings, Matrix Factorizations and Deformations
Abstract:   This talk is concerned with D-branes in topological string theory. After
giving a short introduction to topological strings, I will focus on the
description of topological B-branes in terms of matrix factorizations. A
method to calculate the effective superpotential via deformations of
matrix factorizations will be presented, and applied to a toy example.
Finally, I will discuss possible applications to Calabi-Yau
compactifications and mirror symmetry.

Ilka Brunner (Zurich)
Title:
On defects and their fusion
Abstract: I will discuss defects in two-dimensional conformal field theories.
Defects are one-dimensional interfaces separating two (in general
different) conformal field theories. Two defects can "merge" to form
a new defect, and likewise defects can act on boundary conditions
in a natural way. I will explain these operations in examples and
discuss possible applications.

Radu Roiban (Penn State U.)
Title:  The cusp anomalous dimension at weak and strong coupling in N=4 super-Yang-Mills theory
Abstract: The cusp anomalous dimension in any gauge theory governs both the IR behavior of scattering amplitudes as well as the RG flow of a certain local operator. We review the Bethe ansatz approach to the calculation of anomalous dimensions of local operators in the maximally supersymmetric Yang-Mills theory in four dimensions and the cusp anomalous dimension that follows from it both at weak and string coupling. Using the AdS/CFT correspondence, the strong coupling results are tested by higher loop  calculation  in the world sheet theory for strings in AdS5xS**5.

Werner Nahm  (DIAS, Dublin)
Title:  Finite size corrections to the thermodynamic Bethe ansatz
Abstract: Luescher's approach to finite size corrections is compared with Teschner's formula for the sinh-Gordon model.

Mohab Abou-Zeid
(Vrije U., Brussels)
Title: "Twistor Strings and Supergravity"
Abstract: "I will present a modification of the Berkovits twistor string theory which gives the spectrum of Einstein (super)gravity coupled to (super) Yang-Mills.  The world-sheet formulation of the Berkovits model involves so-called beta-gamma systems; I will describe the symmetries of such systems and their gauging, and explain how the analysis can be applied to the construction of a family of new gauged Berkovits twistor strings which are free from world-sheet anomalies. I will describe the corresponding spectra in space-time, and show that they lead to Einstein supergravities instead of the higher derivative conformal supergravities arising in the original twistor string models of Witten and Berkovits. The new theories include one with the spectrum of N=8 supergravity, two theories with the spectrum of N=4 supergravity coupled to N=4 Yang-Mills, a family of N>0 models with the spectra of self-dual
supergravity coupled to self-dual super-Yang-Mills, and a non-supersymmetric string with the spectrum of self-dual gravity coupled to self-dual Yang-Mills and a scalar. Time permitting, I will briefly discuss what is known about the interactions."

Volker Schomerus (DESY)
Title: String duality in curved backgrounds
Abstract: Perturbative string theory possesses genuinely stringy symmetries, known as T-dualities. These have been studied extensively in the past because of their important implications for string physics as well as for computations. Applications of modern string theory mostly involve curved backgrounds, possibly with fluxes, whose duality symmetries have remained largely unexplored. At the example of strings moving in the Euclidean $AdS_3$ I will present a duality with rather novel features. By an intriguing mechanism it relates the original 3-dimensional curved background with string propagation in a 1-dimensional exponential potential. Several applications and relations with other recent developments will be sketched.

Gabriele Travaglini (Queen Mary, U.)
Title: Twistors, scattering amplitudes, and Wilson loops
Abstract: In this talk I will review recent advances in calculating scattering amplitudes in gauge theory (with and without supersymmetry) without making use of Feynman diagrams. The MHV diagram method, and its applications at loop level, will be discussed with particular reference to non-supersymmetric gauge theory. In the last part of my talk I will describe a recent Wilson loop calculation at weak coupling, where the loop is bounded by the
n-segment Alday-Maldacena contour. Quite surprisingly, the vacuum expectation value of this Wilson loops leads to the infinite sequence of MHV amplitudes in N=4 super Yang-Mills.

Romuald Janik
(Jagiellonian U.)
Title: Wrapping interactions and finite size effects
Abstract: Anomalous dimensions of long operators in SYM are described by the asymptotic Bethe ansatz. There exist, in addition, finite size effects due to wrapping interactions. In this talk I would like to show that within the AdS/CFT correspondence these additional wrapping interactions are described by finite size corrections in the relevant integrable quantum field theory.

Lilia Anguelova (Queen Mary, U.)
Title: O'KKLT at Finite Temperature

Abstract: Moduli stabilization is a crucial step on the road to relating string
compactifications and phenomenology. To achieve it, it is essential to
consider nonzero background fluxes and to also take into account certain
quantum effects. However, the result is usually a supersymmetric ground
state. Understanding how it can be lifted to a dS vacuum is a rather
non-trivial additional problem. It was recently realized that this
problem can be resolved by coupling to a field theory sector that exhibits
metastable dynamical susy breaking. This set-up however raises the
question: How natural is it for a system to be in a metastable state
rather than in its global vacuum? The answer turns out to be in the
specifics of the evolution of the system at finite temperature. We address
these issues in the context of a particular model with a dS vacuum and
stabilized moduli, namely the KKLT-O'Raifeartaigh (called for brevity
O'KKLT) model.

Fernando Quevedo (Cambridge)

Title: Phenomenological and Cosmological implications of LARGE volume
string compactifications

Contact:

Sergey Frolov

Office: 3.4 Hamilton Building, Trinity College

Phone: +353 1 896 4027

E-mail: frolovs@maths.tcd.ie

### Year 2006-2007

 Month Date Speaker Title September 14 Tamas Hausel (Oxford) Mixed Hodge Polynomials of Character Varieties October 9 Samson Shatashvili (Trinity College Dublin) Higgs Bundles, Gauge Theories  and Quantum Groups October 16 no seminar because of RIA Hamilton Lecture at 7.15pm October 23 Matthias Staudacher (Albert-Einstein Institute, Potsdam) Large Spin Twist Operators, Gluon Amplitudes, and AdS/CFT October 30 bank holiday November 6 Stefano Kovacs (Trinity College Dublin) Ultra-violet finiteness of planar beta-deformed Yang-Mills November 13 Maria Paola Lombardo (INFN, Frascati) Quark Gluon Plasma, and the phases of QCD in the T, \mu^2 plane November 20 Michael Green (Cambridge) Nonrenormalization in string theory and M-theory November 27 Gleb Arutyunov (Utrecht) The off-shell symmetry algebra of the light-cone AdS_5 x S^5 superstring December 4 Yasha Shnir (Institute of Physics, Oldenburg) Monopole-antimonopole chains and closed vortices in Yang-Mills-Higgs and Einstein-Yang-Mills-Higgs theory December 11 winter break December 18 winter break December 25 winter break January 1 winter break January 8 Tristan McLoughlin (Penn State U.) Worldsheet Scattering and AdS/CFT January 17 Alastair King (University of Bath) Dimers and non-commutative Calabi-Yau 3-folds January 22 Arkady Tseytlin  (Imperial College) Sigma model RG flow  and Perelman's entropy January 29 Neil Lambert (King's College) The M-theory Geometry of Fermionic Open String Modes February 5 Simon Hands (Swansea) Lattice QCD approach to Quark Matter February 12 Kelly Stelle (Imperial College) Is N=8 Supergravity finite? The debate about UV divergences in maximal Super Yang Mills and Supergravity theories. February 19 Vladimir Kazakov (Ecole Normal, Paris) Supersymmetric Bethe Ansatz and Baxter Equations from Discrete Hirota Dynamics February 26 Anne Taormina (Durham) Liouville field, Modular forms and Elliptic genera March 5 Manfred Herbst (DESY) Phases of N=2 theories in two dimensions with boundary March 12 spring break March 19 spring break March 26 spring break April 2 O Colgain, Eoin (Imperial College) 4d CFTS with M-theory duals April 9 holiday April 16 Lionel Mason (Oxford) From twistor-strings to quantum gravity April 23 Rainer Sommer (DESY Zeuthen) Nonperturbative Heavy Quark Effective Theory April 30 Sergey Cherkis (TCD) Instantons on Gravitons May 3 Eliezer Rabinovici (The Hebrew University) Little Hagedorn Holography May 7 holiday May 14 summer break

# Titles and Abstracts of Talks

Sergey Cherkis (TCD)

Instantons on Gravitons

We present a construction of Yang-Mills Instantons on
Asymptotically Locally Flat Gravitational Instantons.  To illustrate
the construction we explicitly compute the metric on the moduli space
of one instanton on Taub-NUT space and find the one instanton
solution.  These results can be applied to the study of the
supersymmetric inhomogeneity theories as well as to N=4 three-
dimensional Seiberg-Witten theories.

Eliezer Rabinovici
(The Hebrew University)

Little Hagedorn Holography

We disucss the issue of a Hagedorn spectrum in Little String Theory.

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Rainer Sommer (DESY Zeuthen)

Nonperturbative Heavy Quark Effective Theory

The future of flavour physics will require higher
and higher precision in order to determine the
standard model quark mixing matrix and in particular
to uncover contributions of physics beyond the
standard model. A rather precise knowledge of
hadronic matrix elements will be necessary to
make full use of the available experimental
information. Lattice gauge theory offers the
computational tool to compute a number of these
matrix elements.
We discuss the challenges that lattice gauge theories
are facing, in particular in the treatment of
beauty quarks. The development of a fully non-perturbative
formulation of Heavy Quark Effective Theory will
be explained in detail. This includes the determination
of the parameters of the effective theory from QCD,
thus preserving the predictivity of QCD.

Lionel Mason
(Oxford)

From twistor-strings to quantum gravity

O Colgain, Eoin  (Imperial College)

4d CFTS with M-theory duals

In this talk we return to the most general supersymmetric solutions of  D=11 supergravity with AdS_5 factors from which the Sasaki-Einstein spaces Y^{p,q} were discovered. For explicit solutions, including the Y^{p,q} subclass, we calculate the central charges and also the conformal
dimensions of certain chiral primary operators arising from wrapped membranes. For the most general class of solutions
we will show that there is a consistent Kaluza-Klein truncation to minimal D=5 gauged supergravity. This latter result allows
us to study some aspects of the dual strongly coupled thermal plasma with a non-zero R-charge chemical potential and, in particular, we show that the ratio of the shear viscosity to the entropy density has the universal value of 1/4\pi.

Manfred Herbst
(DESY)

Phases of N=2 theories in two dimensions with boundary

N=(2,2) gauged linear sigma model in two dimensions provided a quite
efficient concept for describing geometric transitions like flops between
Calabi--Yau manifolds and even transitions to non-geometric models such as
Landau--Ginzburg orbifold. In this talk we will consider B-type D-branes
in these models and study, in particular, their behaviour under
deformations of the Kaehler moduli.

Anne Taormina (Durham)

Liouville field, Modular forms and Elliptic genera

The elliptic genus of the K3 surface yields, in the
decompactification limit of the surface,
a candidate formula for the elliptic genus of the singular A_1 ALE space.
We generalize this elliptic genus to A_N ALE spaces and show it coincides
with the expression obtained when pairing the N=2 minimal and N=2
Liouville theories.

Vladimir Kazakov (Ecole Normal, Paris)

Supersymmetric Bethe Ansatz and Baxter Equations from Discrete
Hirota Dynamics

We show that eigenvalues of the family of Baxter Q-operators for
supersymmetric integrable spin chains constructed with the
gl(K|M)-invariant R-matrix obey the Hirota bilinear difference
equation. The nested Bethe ansatz for super spin chains, with any
choice of simple root system, is then treated as a discrete
dynamical system for zeros of polynomial solutions to the Hirota
equation. Our basic tool is a chain of Backlund transformations
for the Hirota equation connecting quantum transfer matrices.
This approach also provides a systematic way to derive the
generalized Baxter equations for super spin chains.

Simon Hands (Swansea)

Lattice QCD approach to Quark Matter

I will give a brief survey of the exotic phenomena expected in systems
with very very high baryon density such as the cores of neutron stars. I
then review difficulties in applying numerical simulations of lattice QCD,
the orthodox approach to quantitative calculations in strong interaction
physics, to systems with non-zero baryon number - and motivate the
viewpoint that the problem will not be solved simply by increases in
computer power. Finally I review recent progress in simulations of a
related but simpler theory, Two Color QCD, and argue that in the high
density regime it may yield important lessons for the physical theory.

Neil Lambert (King's College)

The M-theory Geometry of Fermionic Open String Modes

We will discuss the lift to M-theory of a D4-D6 intersection. In
particular the open string that stretches between to D4 and D6 branes gives
rise to a charged chiral Fermion. We discuss the appearance of this mode in the
M5-brane worldvolume theory as well as some interesting features associated
with its interpretation.

Arkady Tseytlin (Imperial College London)

Sigma model RG flow  and Perelman's entropy

Zamolodchikov's c-theorem type argument  implies  that the RG flow in
2d sigma model should be gradient one to all loop orders. However, the
monotonicity of the flow of the target-space metric is not obvious.
To leading  order when the RG flow is simply the Ricci flow the
monotonicity was proved by Perelman by constructing an entropy''
functional which is essentially a metric-dilaton action with a
condition that the target-space volume is fixed. We will  discuss how
to generalize the Perelman's construction to all loop orders.
The resulting `entropy'' is equal to minus the central charge at the
fixed points, in agreement with the general claim of the c-theorem.

Tristan McLoughlin (Penn State U.)

Worldsheet Scattering and AdS/CFT

The realization that both the worldsheet theory on AdS_5xS^5 and
N=4 SYM can, in certain limits, be described by integrable systems
has lead to a good deal of recent progress in understanding
the AdS/CFT correspondence.
In this talk we will review the perturbative construction of the
worldsheet S-matrix in the light-cone gauge and discuss the realization of
the global symmetries on asymptotic states. A mild non-locality of the
supercharges results in the natural appearance of a non-trivial coproduct
and we will outline how the symmetries form a Hopf algebra. At leading
order this scattering matrix can be compared with the well known
conjectures for the all-loop asymptotic S-matrix that enters the Bethe
equations for gauge theory anomalous dimensions and we will show that they
are in good agreement. This S-matrix provides a convenient description of
the two theories and should eventually allow us to compare the complete
spectrum on both sides of the duality. Further, we will outline some
partial attempts to extend this equivalence, and the corresponding
integrable structures, to include worldsheet quantum loop effects.

Alastair King  (University of Bath)

Dimers and non-commutative Calabi-Yau 3-folds

Dimer models, introduced by Hanany et al, are expected to
provide non-commutative crepant resolutions of toric 3-fold Gorenstein
singularities. This is an introductory talk which will discuss what these
terms mean and why the expectation is reasonable.

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Matthias Staudacher

Albert-Einstein Institute, Potsdam

Large Spin Twist Operators, Gluon Amplitudes, and AdS/CFT

We discuss recent developments in relating the anomalous dimensions

of large spin twist operators in N=4 gauge theory to (a) space time

gluon amplitude calculations and to (b) string theory via the

AdS/CFT correspondence.

Stefano Kovacs

Trinity College Dublin

Ultra-violet finiteness of planar beta-deformed Yang-Mills

I will discuss a marginal deformation of N=4 Yang-Mills. This theory,

usually referred to as beta-deformed N=4 super Yang-Mills, has only

N=1 supersymmetry and a U(1)xU(1) flavour symmetry. I will show that

the introduction of a suitably defined superspace star-product allows

to formulate the theory in N=4 light-cone superspace. I will then use

this formulation to show that the theory is conformally invariant, in

the planar approximation, by proving that its Green functions are

ultra-violet finite to all orders in perturbation theory.

Maria Paola Lombardo

Istituto Nazionale di Fisica Nucleare, Frascati(Roma) Italy

Quark Gluon Plasma, and the phases of QCD in the T, $\mu^2$ plane.

At high temperature and/or baryon density QCD undergoes a

transition to a new phase, whose properties are under

theoretical and experimental investigations.

By use of an imaginary $\mu$ -- which avoids the sign problem of

finite density QCD -- we can explore a relatively large region of

the QCD phase diagram in the T, $\mu$^2 plane, including

the highly non--perturbative  phase $T_c < T < 2 T_c$. In the first

part of the talk I will introduce the various methods for analytic

continuation from imaginary to real chemical potential, and discuss

the results for the critical line. In the second part I will focus

on the hot region, where the consideration of the critical behaviour

at imaginary chemical potential affords a new, simple description

of the properties of the strongly interactive Quark Gluon Plasma.

Michael Green
(Cambridge)

"Nonrenormalization in string theory and M-theory".

The study of Feynman diagrams of eleven-dimensional supergravity leads to
detailed statements concerning non-perturbative features of the low energy
limit of string theory in lower dimensions.  Together with certain
well-established duality relationships this gives rise to some powerful
nonrenormalization statements that suggest that supergravity itself has
milder ultraviolet divergences than might have been expected.

Gleb Arutyunov (Utrecht)

The off-shell symmetry algebra of the light-cone AdS_5 x S^5 superstring

We analyze the psu(2,2|4) supersymmetry algebra of a superstring propagating
in the AdS_5 x S^5 background in the uniform light-cone gauge.
We consider the off-shell theory by relaxing the level-matching condition
and take the limit of infinite light-cone momentum, which decompactifies the
string world-sheet.
We focus on the psu(2|2)+psu(2|2) subalgebra which leaves the light-cone
Hamiltonian invariant and show that it undergoes extension by a central
element which is expressed in terms of the level-matching operator.
This result is in agreement with the conjectured symmetry algebra of the
dynamic S-matrix in the dual N=4 gauge theory

Yasha Shnir  (Institute of Physics, Oldenburg)

Monopole-antimonopole chains and closed vortices in Yang-Mills-Higgs and
Einstein-Yang-Mills-Higgs theory.

We discuss properties of the axially symmetric static saddle point
solutions of SU(2) Yang-Mills-Higgs theory which represent composite
states of monopoles and antimonopoles and/or vortex rings. They are either
deformations of the topologically trivial sector or deformations of the
axially symmetric charge n multimonopole. The energy of these
configurations exceeds the Bogomol'nyi bound even in the limit of
vanishing scalar coupling. When the theory is coupled with gravity new
branches of the graviting monopoles/vortices emerges smoothly from these
flat space configurations. We discuss interpretation of the upper branche
configuration as a composite system consisting of Bartnik-McKinnon
solution of EYM theory and an outer multimonopole/vortex solution of the
EYMH theory.

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