1,080 research outputs found
Gauging of Geometric Actions and Integrable Hierarchies of KP Type
This work consist of two interrelated parts. First, we derive massive
gauge-invariant generalizations of geometric actions on coadjoint orbits of
arbitrary (infinite-dimensional) groups with central extensions, with gauge
group being certain (infinite-dimensional) subgroup of . We show that
there exist generalized ``zero-curvature'' representation of the pertinent
equations of motion on the coadjoint orbit. Second, in the special case of
being Kac-Moody group the equations of motion of the underlying gauged WZNW
geometric action are identified as additional-symmetry flows of generalized
Drinfeld-Sokolov integrable hierarchies based on the loop algebra {\hat \cG}.
For {\hat \cG} = {\hat {SL}}(M+R) the latter hiearchies are equivalent to a
class of constrained (reduced) KP hierarchies called {\sl cKP}_{R,M}, which
contain as special cases a series of well-known integrable systems (mKdV, AKNS,
Fordy-Kulish, Yajima-Oikawa etc.). We describe in some detail the loop algebras
of additional (non-isospectral) symmetries of {\sl cKP}_{R,M} hierarchies.
Apart from gauged WZNW models, certain higher-dimensional nonlinear systems
such as Davey-Stewartson and -wave resonant systems are also identified as
additional symmetry flows of {\sl cKP}_{R,M} hierarchies. Along the way we
exhibit explicitly the interrelation between the Sato pseudo-differential
operator formulation and the algebraic (generalized) Drinfeld-Sokolov
formulation of {\sl cKP}_{R,M} hierarchies. Also we present the explicit
derivation of the general Darboux-B\"acklund solutions of {\sl cKP}_{R,M}
preserving their additional (non-isospectral) symmetries, which for R=1 contain
among themselves solutions to the gauged WZNW field
equations.Comment: LaTeX209, 47 page
The AdS(5)xS(5) Semi-Symmetric Space Sine-Gordon Theory
The generalized symmetric space sine-Gordon theories are a series of
1+1-integrable field theories that are classically equivalent to superstrings
on symmetric space spacetimes F/G. They are formulated in terms of a
semi-symmetric space as a gauged WZW model with fermions and a potential term
to deform it away from the conformal fixed point. We consider in particular the
case of PSU(2,2|4)/Sp(2,2)xSp(4) which corresponds to AdS(5)xS(5). We argue
that the infinite tower of conserved charges of these theories includes an
exotic N=(8,8) supersymmetry that is realized in a mildy non-local way at the
Lagrangian level. The supersymmetry is associated to a double central extension
of the superalgebra psu(2|2)+psu(2|2) and includes a non-trivial R symmetry
algebra corresponding to global gauge transformations, as well as 2-dimensional
spacetime translations. We then explicitly construct soliton solutions and show
that they carry an internal moduli superspace CP(2|1)xCP(2|1) with both bosonic
and Grassmann collective coordinates. We show how to semi-classical quantize
the solitons by writing an effective quantum mechanical system on the moduli
space which takes the form of a co-adjoint orbit of SU(2|2)xSU(2|2). The
spectrum consists of a tower of massive states in the short, or atypical,
symmetric representations, just as the giant magnon states of the string world
sheet theory, although here the tower is truncated.Comment: 39 pages, references adde
On the Moduli Space of SU(3) Seiberg-Witten Theory with Matter
We present a qualitative model of the Coulomb branch of the moduli space of
low-energy effective N=2 SQCD with gauge group SU(3) and up to five flavours of
massive matter. Overall, away from double cores, we find a situation broadly
similar to the case with no matter, but with additional complexity due to the
proliferation of extra BPS states. We also include a revised version of the
pure SU(3) model which can accommodate just the orthodox weak coupling
spectrum.Comment: 32 pages, 25 figures, uses JHEP.cls, added references, deleted joke
Phase Transitions of Orientifold Gauge Theories at Large N in Finite Volume
In this paper we consider the phase structure of ``orientifold'' gauge
theories--obtained from unitary supersymmetric gauge theories by replacing
adjoint Majorana fermions by Dirac fermions in the symmetric or anti-symmetric
representations--in finite volume S^3 x S^1. If the radius of the S^3 is small
the calculations can be performed at weak coupling for any value of the S^1
radius. We demonstrate that there is a confinement/de-confining type of phase
transition even when the fermions have periodic (non-thermal) boundary
conditions around S^1. At small radius of S^1, the theory is in a phase where
charge conjugation and large non-periodic gauge transformation are
spontaneously broken. But for large radius of S^1 the phase preseves these
symmetries just as in the related supersymmetric theory.Comment: 12 page
Topology change in commuting saddles of thermal N=4 SYM theory
We study the large N saddle points of weakly coupled N=4 super Yang-Mills
theory on S^1 x S^3 that are described by a commuting matrix model for the
seven scalar fields {A_0, \Phi_J}. We show that at temperatures below the
Hagedorn/`deconfinement' transition the joint eigenvalue distribution is S^1 x
S^5. At high temperatures T >> 1/R_{S^3}, the eigenvalues form an ellipsoid
with topology S^6. We show how the deconfinement transition realises the
topology change S^1 x S^5 --> S^6. Furthermore, we find compelling evidence
that when the temperature is increased to T = 1/(\sqrt\lambda R_{S^3}) the
saddle with S^6 topology changes continuously to one with S^5 topology in a new
second order quantum phase transition occurring in these saddles.Comment: 1+40 pages, 6 figures. v2: Title changed. Status of commuting saddles
clarified: New high T phase transition claimed in the commuting sector only,
not in the full theor
Causality, renormalizability and ultra-high energy gravitational scattering
The amplitude A(s,t) for ultra-high energy scattering can be found in the
leading eikonal approximation by considering propagation in an Aichelburg-Sexl
gravitational shockwave background. Loop corrections in the QFT describing the
scattered particles are encoded for energies below the Planck scale in an
effective action which in general exhibits causality violation and Shapiro time
advances. In this paper, we use Penrose limit techniques to calculate the full
energy dependence of the scattering phase shift Theta_scat(hat_s},, where the
single variable hat_s = Gs/m^2 b^(d-2) contains both the CM energy s and impact
parameter b, for a range of scalar QFTs in d dimensions with different
renormalizability properties. We evaluate the high-energy limit of
Theta_scat(hat_s) and show in detail how causality is related to the existence
of a well-defined UV completion. Similarities with graviton scattering and the
corresponding resolution of causality violation in the effective action by
string theory are briefly discussed.Comment: 23 page
Quantum integrability of sigma models on AII and CII symmetric spaces
Exact massive S-matrices for two dimensional sigma models on symmetric spaces
SU(2N)/Sp(N) and Sp(2P)/Sp(P)*Sp(P) are conjectured. They are checked by
comparison of perturbative and non perturbative TBA calculations of free energy
in a strong external field. We find the mass spectrum of the models and
calculate their exact mass gap.Comment: 11 p., minor correction
Bound States of the q-Deformed AdS5 x S5 Superstring S-matrix
The investigation of the q deformation of the S-matrix for excitations on the
string world sheet in AdS5 x S5 is continued. We argue that due to the lack of
Lorentz invariance the situation is more subtle than in a relativistic theory
in that the nature of bound states depends on their momentum. At low enough
momentum |p|<E the bound states transform in the anti-symmetric representation
of the super-algebra symmetry and become the solitons of the Pohlmeyer reduced
theory in the relativistic limit. At a critical momentum |p|=E they become
marginally unstable, and at higher momenta the stable bound states are in the
symmetric representation and become the familiar magnons in the string limit as
q->1. This subtlety fixes a problem involving the consistency of crossing
symmetry with the relativistic limit found in earlier work. With mirror
kinematics, obtained after a double Wick rotation, the bound state structure is
simpler and there are no marginally unstable bound states.Comment: 25 page
Classical and Quantum Solitons in the Symmetric Space Sine-Gordon Theories
We construct the soliton solutions in the symmetric space sine-Gordon
theories. The latter are a series of integrable field theories in
1+1-dimensions which are associated to a symmetric space F/G, and are related
via the Pohlmeyer reduction to theories of strings moving on symmetric spaces.
We show that the solitons are kinks that carry an internal moduli space that
can be identified with a particular co-adjoint orbit of the unbroken subgroup H
of G. Classically the solitons come in a continuous spectrum which encompasses
the perturbative fluctuations of the theory as the kink charge becomes small.
We show that the solitons can be quantized by allowing the collective
coordinates to be time-dependent to yield a form of quantum mechanics on the
co-adjoint orbit. The quantum states correspond to symmetric tensor
representations of the symmetry group H and have the interpretation of a fuzzy
geometric version of the co-adjoint orbit. The quantized finite tower of
soliton states includes the perturbative modes at the base.Comment: 53 pages, additional comments and small errors corrected, final
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