111 research outputs found
Center-stabilized Yang-Mills theory: confinement and large volume independence
We examine a double trace deformation of SU(N) Yang-Mills theory which, for
large and large volume, is equivalent to unmodified Yang-Mills theory up to
corrections. In contrast to the unmodified theory, large volume
independence is valid in the deformed theory down to arbitrarily small volumes.
The double trace deformation prevents the spontaneous breaking of center
symmetry which would otherwise disrupt large volume independence in small
volumes. For small values of , if the theory is formulated on with a sufficiently small compactification size , then an analytic
treatment of the non-perturbative dynamics of the deformed theory is possible.
In this regime, we show that the deformed Yang-Mills theory has a mass gap and
exhibits linear confinement. Increasing the circumference or number of
colors decreases the separation of scales on which the analytic treatment
relies. However, there are no order parameters which distinguish the small and
large radius regimes. Consequently, for small the deformed theory provides
a novel example of a locally four-dimensional pure gauge theory in which one
has analytic control over confinement, while for large it provides a simple
fully reduced model for Yang-Mills theory. The construction is easily
generalized to QCD and other QCD-like theories.Comment: 29 pages, expanded discussion of multiple compactified dimension
Continuity, Deconfinement, and (Super) Yang-Mills Theory
We study the phase diagram of SU(2) Yang-Mills theory with one adjoint Weyl
fermion on R^3xS^1 as a function of the fermion mass m and the compactification
scale L. This theory reduces to thermal pure gauge theory as m->infinity and to
circle-compactified (non-thermal) supersymmetric gluodynamics in the limit
m->0. In the m-L plane, there is a line of center symmetry changing phase
transitions. In the limit m->infinity, this transition takes place at
L_c=1/T_c, where T_c is the critical temperature of the deconfinement
transition in pure Yang-Mills theory. We show that near m=0, the critical
compactification scale L_c can be computed using semi-classical methods and
that the transition is of second order. This suggests that the deconfining
phase transition in pure Yang-Mills theory is continuously connected to a
transition that can be studied at weak coupling. The center symmetry changing
phase transition arises from the competition of perturbative contributions and
monopole-instantons that destabilize the center, and topological molecules
(neutral bions) that stabilize the center. The contribution of molecules can be
computed using supersymmetry in the limit m=0, and via the
Bogomolnyi--Zinn-Justin (BZJ) prescription in the non-supersymmetric gauge
theory. Finally, we also give a detailed discussion of an issue that has not
received proper attention in the context of N=1 theories---the non-cancellation
of nonzero-mode determinants around supersymmetric BPS and KK
monopole-instanton backgrounds on R^3xS^1. We explain why the non-cancellation
is required for consistency with holomorphy and supersymmetry and perform an
explicit calculation of the one-loop determinant ratio.Comment: A discussion of the non-cancellation of the nonzero mode determinants
around supersymmetric monopole-instantons in N=1 SYM on R^3xS^1 is added,
including an explicit calculation. The non-cancellation is, in fact, required
by supersymmetry and holomorphy in order for the affine-Toda superpotential
to be reproduced. References have also been adde
Testing a novel large-N reduction for N=4 super Yang-Mills theory on RxS^3
Recently a novel large-N reduction has been proposed as a maximally
supersymmetric regularization of N=4 super Yang-Mills theory on RxS^3 in the
planar limit. This proposal, if it works, will enable us to study the theory
non-perturbatively on a computer, and hence to test the AdS/CFT correspondence
analogously to the recent works on the D0-brane system. We provide a nontrivial
check of this proposal by performing explicit calculations in the large-N
reduced model, which is nothing but the so-called plane wave matrix model,
around a particular stable vacuum corresponding to RxS^3. At finite temperature
and at weak coupling, we reproduce precisely the deconfinement phase transition
in the N=4 super Yang-Mills theory on RxS^3. This phase transition is
considered to continue to the strongly coupled regime, where it corresponds to
the Hawking-Page transition on the AdS side. We also perform calculations
around other stable vacua, and reproduce the phase transition in super
Yang-Mills theory on the corresponding curved space-times such as RxS^3/Z_q and
RxS^2.Comment: 24 pages, 4 figure
Volume independence in large Nc QCD-like gauge theories
Volume independence in large \Nc gauge theories may be viewed as a
generalized orbifold equivalence. The reduction to zero volume (or Eguchi-Kawai
reduction) is a special case of this equivalence. So is temperature
independence in confining phases. In pure Yang-Mills theory, the failure of
volume independence for sufficiently small volumes (at weak coupling) due to
spontaneous breaking of center symmetry, together with its validity above a
critical size, nicely illustrate the symmetry realization conditions which are
both necessary and sufficient for large \Nc orbifold equivalence. The
existence of a minimal size below which volume independence fails also applies
to Yang-Mills theory with antisymmetric representation fermions [QCD(AS)].
However, in Yang-Mills theory with adjoint representation fermions [QCD(Adj)],
endowed with periodic boundary conditions, volume independence remains valid
down to arbitrarily small size. In sufficiently large volumes, QCD(Adj) and
QCD(AS) have a large \Nc ``orientifold'' equivalence, provided charge
conjugation symmetry is unbroken in the latter theory. Therefore, via a
combined orbifold-orientifold mapping, a well-defined large \Nc equivalence
exists between QCD(AS) in large, or infinite, volume and QCD(Adj) in
arbitrarily small volume. Since asymptotically free gauge theories, such as
QCD(Adj), are much easier to study (analytically or numerically) in small
volume, this equivalence should allow greater understanding of large \Nc QCD
in infinite volume.Comment: 32 pages, 4 figure
Various Super Yang-Mills Theories with Exact Supersymmetry on the Lattice
We continue to construct lattice super Yang-Mills theories along the line
discussed in the previous papers \cite{sugino, sugino2}. In our construction of
theories in four dimensions, the problem of degenerate vacua
seen in \cite{sugino} is resolved by extending some fields and soaking up
would-be zero-modes in the continuum limit, while in the weak coupling
expansion some surplus modes appear both in bosonic and fermionic sectors
reflecting the exact supersymmetry. A slight modification to the models is made
such that all the surplus modes are eliminated in two- and three-dimensional
models obtained by dimensional reduction thereof. models in
three dimensions need fine-tuning of three and one parameters respectively to
obtain the desired continuum theories, while two-dimensional models with do not require any fine-tuning.Comment: 28 pages, no figure, LaTeX, JHEP style; (v2) published version to
JHEP; (v3) argument on the vacuum degeneracy revised, 34 page
The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
We study the dynamics of four dimensional gauge theories with adjoint
fermions for all gauge groups, both in perturbation theory and
non-perturbatively, by using circle compactification with periodic boundary
conditions for the fermions. There are new gauge phenomena. We show that, to
all orders in perturbation theory, many gauge groups are Higgsed by the gauge
holonomy around the circle to a product of both abelian and nonabelian gauge
group factors. Non-perturbatively there are monopole-instantons with fermion
zero modes and two types of monopole-anti-monopole molecules, called bions. One
type are "magnetic bions" which carry net magnetic charge and induce a mass gap
for gauge fluctuations. Another type are "neutral bions" which are magnetically
neutral, and their understanding requires a generalization of multi-instanton
techniques in quantum mechanics - which we refer to as the
Bogomolny-Zinn-Justin (BZJ) prescription - to compactified field theory. The
BZJ prescription applied to bion-anti-bion topological molecules predicts a
singularity on the positive real axis of the Borel plane (i.e., a divergence
from summing large orders in peturbation theory) which is of order N times
closer to the origin than the leading 4-d BPST instanton-anti-instanton
singularity, where N is the rank of the gauge group. The position of the
bion--anti-bion singularity is thus qualitatively similar to that of the 4-d IR
renormalon singularity, and we conjecture that they are continuously related as
the compactification radius is changed. By making use of transseries and
Ecalle's resurgence theory we argue that a non-perturbative continuum
definition of a class of field theories which admit semi-classical expansions
may be possible.Comment: 112 pages, 7 figures; v2: typos corrected, discussion of
supersymmetric models added at the end of section 8.1, reference adde
Seiberg-Witten and "Polyakov-like" magnetic bion confinements are continuously connected
We study four-dimensional N=2 supersymmetric pure-gauge (Seiberg-Witten)
theory and its N=1 mass perturbation by using compactification S**1 x R**3. It
is well known that on R**4 (or at large S**1) the perturbed theory realizes
confinement through monopole or dyon condensation. At small S**1, we
demonstrate that confinement is induced by a generalization of Polyakov's
three-dimensional instanton mechanism to a locally four-dimensional theory -
the magnetic bion mechanism - which also applies to a large class of
nonsupersymmetric theories. Using a large- vs. small-L Poisson duality, we show
that the two mechanisms of confinement, previously thought to be distinct, are
in fact continuously connected.Comment: 49 pages, 5 figure
Large-N spacetime reduction and the sign and silver-blaze problems of dense QCD
We study the spacetime-reduced (Eguchi-Kawai) version of large-N QCD with
nonzero chemical potential. We explore a method to suppress the sign
fluctuations of the Dirac determinant in the hadronic phase; the method employs
a re-summation of gauge configurations that are related to each other by center
transformations. We numerically test this method in two dimensions, and find
that it successfully solves the silver-blaze problem. We analyze the system
further, and measure its free energy F, the average phase theta of its Dirac
determinant, and its chiral condensate . We show that F and
are independent of mu in the hadronic phase but that, as chiral
perturbation theory predicts, the quenched chiral condensate drops from its
mu=0 value when mu~(pion mass)/2. Finally, we find that the distribution of
theta qualitatively agrees with further, more recent, predictions from chiral
perturbation theory.Comment: 43 pages, 17 figure
The AdS/QCD Correspondence: Still Undelivered
We consider the particle spectrum and event shapes in large N gauge theories
in different regimes of the short-distance 't Hooft coupling, lambda. The
mesons in the small lambda limit should have a Regge spectrum in order to agree
with perturbation theory, while generically the large lambda theories with
gravity duals produce spectra reminiscent of KK modes. We argue that these
KK-like states are qualitatively different from QCD modes: they are deeply
bound states which are sensitive to short distance interactions rather than the
flux tube-like states expected in asymptotically free, confining gauge
theories. In addition, we also find that the characteristic event shapes for
the large lambda theories with gravity duals are close to spherical, very
different from QCD-like (small lambda, small N) and Nambu-Goto-like (small
lambda, large N) theories which have jets. This observation is in agreement
with the conjecture of Strassler on event shapes in large 't Hooft coupling
theories, which was recently proved by Hofman and Maldacena for the conformal
case. This conclusion does not change even when considering soft-wall
backgrounds in the gravity dual. The picture that emerges is the following:
theories with small and large lambda are qualitatively different, while
theories with small and large N are qualitatively similar. Thus it seems that
it is the relative smallness of the 't Hooft coupling in QCD that prevents a
reliable AdS/QCD correspondence from emerging, and that reproducing
characteristic QCD-like behavior will require genuine stringy dynamics to be
incorporated into any putative dual theory.Comment: 32 pages, 15 figures; references added, minor changes, history
clarifie
Supersymmetric Deformations of Type IIB Matrix Model as Matrix Regularization of N=4 SYM
We construct a supersymmetry and global symmetry
preserving deformation of the type IIB matrix model. This model, without
orbifold projection, serves as a nonperturbative regularization for
supersymmetric Yang-Mills theory in four Euclidean dimensions.
Upon deformation, the eigenvalues of the bosonic matrices are forced to reside
on the surface of a hypertorus. We explicitly show the relation between the
noncommutative moduli space of the deformed matrix theory and the Brillouin
zone of the emergent lattice theory. This observation makes the transmutation
of the moduli space into the base space of target field theory clearer. The
lattice theory is slightly nonlocal, however the nonlocality is suppressed by
the lattice spacing. In the classical continuum limit, we recover the
SYM theory. We also discuss the result in terms of D-branes and
interpret it as collective excitations of D(-1) branes forming D3 branes.Comment: Version 2: Extended discussion of moduli space, added a referenc
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