B. Bringoltz
University of Washington
miller@phys.washington.edu

M. Shifman
University of Minnesota
shifman@umn.edu

M. Unsal
Stanford University
unsal@slac.stanford.edu

L. Yaffe
University of Washington
yaffe@phys.washington.edu

Program Coordinator:
Laura Lee
lee@phys.washington.edu
(206) 685-3509

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Orbifold equivalences for QCD-like theories relating small and large volumes have received much attention in recent years. In order for these orbifold equivalences to be valid, an unbroken Z_N center symmetry is essential. In this talk, we discuss a 3D theory that is related by an orbifold projection to 4D Yang-Mills theory with adjoint fermions, which is thought to keep the center symmetry unbroken even at small volumes. We focus on the necessity of formulating orbifold projections in lattice theories, and highlight the appearance of Wilson-like terms in the continuum 3D theory.

A novel model-independent relation for baryon form factors is discussed. The relation follows from chiral symmetry and the large Nc limit. The relation is applied to the traditional 4D Skyrme model, and to two new 5D holographic models of baryons, the Pomarol-Wulzer model of 5D Skyrmions, and the Sakai-Sugimoto model with baryons as holographic instantons. The 4D Skyrme models and the Pomarol-Wulzer holographic model obey the model-independent relation, but it appears that the Sakai-Sugimoto model does not.

It can be shown that gauge theories at large Nc have a Hagedorn spectrum---the number of hadrons grow exponentially with the mass---provided certain conditions are met. These include certain conditions on the applicability of perturbation for a class of correlation functions at short space-like distances along with confinement in the sense basic sense that there are no isolated color singlet states exist. Notably, the demonstration of a Hagedorn spectrum does not rely on confinement in the sense of an unbroken center symmetry. Using this approach it can be shown that pure Yang-Mills theory as well as theories with fermions in the fundamental, adjoint or anti-fundamental two index representations all have Hagedorn spectra. It is noteworthy that all of these cases have either have a center symmetry explicitly or have an emergent center symmetry which arises at large Nc. This raises the question of whether an unbroken center symmetry is required for the emergence of a Hagedorn spectrum.

I present preliminary results from simulations with dynamical fermions in higher representations. The relevance of these results for models of Dynamical Electroweak Symmetry Breaking are discussed.

The vector meson mass is computed as a function of quark mass in the large N limit of QCD. We use continuum reduction and directly compute the vector meson propagator in momentum space. Quark momentum is inserted using the quenched momentum prescription.

We numerically compute the string tension in the large N limit of three dimensional and four dimensional Yang-Mills theory using Wilson loops. Space-time loops are formed as products of smeared space-like links and unsmeared time-like links. We use continuum reduction and both unfolded and folded Wilson loops in the analysis.

We discuss Dyson instability (change of vacuum when g²- > -g²) from the point of view of the density of states for spin and gauge models with compact groups. We discuss in this context the apparent paradox that in the large-N limit, some expansions in the 't Hooft coupling have a finite radius of convergence. We consider possible implications for a mechanism to terminate de Sitter inflation proposed by Polyakov.

We minimize the one-loop effective potential for SU(N) gauge theories with fermions in various representations. We consider fundamental (F), adjoint (Adj), symmetric (S), and antisymmetric (AS) representation fermions with finite mass m. We calculate the phase diagram as a function of the length of the compact dimension and the fermion mass for various N and Nf . We also consider the effect of periodic boundary conditions [PBC(+)] on fermions as well as antiperiodic boundary conditions [ABC(-)].

Yang-Mills theories in 2+1 (or 3) dimensions are interesting as nontrivial gauge theories in their own right and as effective theories of QCd at high temperatures. By a suitable parametrization of fields and techniques from 2-dimensional CFT, a Hamiltonian approach has been developed which has led to interetsing results on the vacuum wave function, string tension, mass gap, etc. I shall review the basics of this approach, emphasizing symmetries and robustness of results, and also provide a short update on its status. We will indicate a systematic expansion (to be discussed further in A. Yelnikov's talk) for the vacuum wave function. The corrections to the string tension computed in this framework are about 1.2% of the lowest order value.

We consider large N gauge theory on a two dimensional lattice in the presence of a baryonic chemical potential. We work with one copy of naive fermion and argue that reduction holds even in the presence of a chemical potential. Analytical arguments supported by numerical studies show that there is no phase transition as a function of the baryonic chemical potential.

In the large N limit, the SU(N) gauge theory with fermions in the (anti)symmetric representation (orientifold theory) and the SU(N) gauge theory with Majorana fermions in the adjoint representation (adjoint theory) are equivalent in the sector defined by C-invariant bosonic states. This equivalence holds even if the two theories have different global symmetries. I focus on the center symmetry: the adjoint theory is invariant under Z_N, while the orientifold theory only shows a Z₂ symmetry at non-zero temperature. This result is obtained by computing the effective potential of the Polyakov loop in the large-mass expansion on the lattice. In this talk I will sketch the main ideas behind the computation. A physical consequence of the Z₂ symmetry is that both Q-Q and Qbar-Q states exist in the orientifold theory (being Q an external quark in the fundamental representation), while only Qbar-Q states exist in the adjoint theory. I will discuss what orientifold planar equivalence predicts for this states. The generalization to external charges in higher representations will also be discussed.

I will give a nontechnical summary of work with M. Unsal on the index of the Weyl operator on R³xS¹, some remarks on CS theory, and ongoing work on chiral dynamics.

Studies of topological charge distributions in Monte Carlo configurations for both 4-dimensional QCD and 2-dimensional CP(N-1) sigma models has revealed a laminated vacuum structure consisting of alternating sign, codimension one membranes of topological charge. In the CP(N-1) models, the transition from an instanton dominated vacuum at small N to a laminated vacuum dominated by membranes at large N is directly observed to take place at N ≈ 4. For 4-dimensional gauge theory, SU(3) is in the large N, laminated phase. I discuss the holographic relation between the laminated QCD vacuum and a similar structure which arises as the final state of tachyonic decay of an unstable non-BPS Dbrane in IIA string theory. This "tachyonic crystal" consists of an alternating sign array of codimension one Dbranes.

We summarize recent results on the phase structure of reduced models of the Eguchi-Kawai type, and discuss their relevance to the understanding of the physical phases of, and large-N correspondence with, d=4 pure Yang-Mills theories in the planar limit.

I will discuss the current efforts of the Lattice Strong Dynamics collaboration to simulate SU(3) gauge theory with various flavors using large scale lattice simulations with Domain Wall Fermions. The goal of this research is to provide input to LHC phenomenology.

I will discuss some intriguing properties of a recently discovered simple supersymmetric planar system with gauge symmetry. These include: 1) a phase transition in the 't Hooft coupling, 2) exact duality between the strong and weak coupling phases, 3) analytic solutions in the first two fermionic sectors, and 4) equivalences, at strong coupling, with the quantum Heisenberg chain and, independently, with the lattice gas of q-bosons. A new interpretation of the emergence of the phase transition will be also given.

We will show that the KKN calculation of the vacuum wave function for Yang-Mills theory in 2+1 dimensions is in the lowest order of a systematic expansion. Expectation values of observables can be calculated using an effective interacting chiral boson theory, which also leads to a natural expansion as a double series in the coupling constant (to be interpreted within a resummed perturbation series) and a particular kinematical factor. The calculation of the first set of corrections in this expansion shows that the string tension is modified by about 1.2% compared to the lowest order KKN value. This is in reasonable agreement with lattice estimates.

We conjecture that the confinement- deconfinement phase transition in QCD at large number of colors N is triggered by the drastic change in θ behavior. The conjecture is motivated by the holographic model of QCD where confinement -deconfinement phase transition indeed happens precisely at the value of temperature T=T_c where θ dependence experiences a sudden change in behavior. The conjecture is also supported by quantum field theory arguments when the instanton calculations are under complete theoretical control for T > T_c, suddenly break down immediately below T < T_c with sharp changes in the θ dependence. Finally, the conjecture is supported by a number of numerical lattice results. We also discuss a number of other topological defects motivated by holographic picture.