Time-Reversal Breaking in QCD4_4, Walls, and Dualities in 2+1 Dimensions

We study $SU(N)$ Quantum Chromodynamics (QCD) in 3+1 dimensions with $N_f$ degenerate fundamental quarks with mass $m$ and a $\theta$-parameter. For generic $m$ and $\theta$ the theory has a single gapped vacuum. However, as $\theta$ is varied through $\theta=\pi$ for large $m$ there is a first order transition. For $N_f=1$ the first order transition line ends at a point with a massless $\eta'$ particle (for all $N$) and for $N_f>1$ the first order transition ends at $m=0$, where, depending on the value of $N_f$, the IR theory has free Nambu-Goldstone bosons, an interacting conformal field theory, or a free gauge theory. Even when the $4d$ bulk is smooth, domain walls and interfaces can have interesting phase transitions separating different $3d$ phases. These turn out to be the phases of the recently studied $3d$ Chern-Simons matter theories, thus relating the dynamics of QCD$_4$ and QCD$_3$, and, in particular, making contact with the recently discussed dualities in 2+1 dimensions. For example, when the massless $4d$ theory has an $SU(N_f)$ sigma model, the domain wall theory at low (nonzero) mass supports a $3d$ massless $CP^{N_f-1}$ nonlinear $\sigma$-model with a Wess-Zumino term, in agreement with the conjectured dynamics in 2+1 dimensions.Comment: 32 pages. v2: references added, improved discussion of anomalies in Chern-Simons theorie

Quantum Mechanics of the Vacuum State in Two-Dimensional QCD with Adjoint Fermions

A study of two-dimensional QCD on a spatial circle with Majorana fermions in the adjoint representation of the gauge groups SU(2) and SU(3) has been performed. The main emphasis is put on the symmetry properties related to the homotopically non-trivial gauge transformations and the discrete axial symmetry of this model. Within a gauge fixed canonical framework, the delicate interplay of topology on the one hand and Jacobians and boundary conditions arising in the course of resolving Gauss's law on the other hand is exhibited. As a result, a consistent description of the residual $Z_N$ gauge symmetry (for SU(N)) and the ``axial anomaly" emerges. For illustrative purposes, the vacuum of the model is determined analytically in the limit of a small circle. There, the Born-Oppenheimer approximation is justified and reduces the vacuum problem to simple quantum mechanics. The issue of fermion condensates is addressed and residual discrepancies with other approaches are pointed out.Comment: 44 pages; for hardcopies of figures, contact [email protected]

Brane Dynamics and 3D Seiberg Duality on the Domain Walls of 4D N=1 SYM

We study a three-dimensional U(k) Yang-Mills Chern-Simons theory with adjoint matter preserving two supersymmetries. According to Acharya and Vafa, this theory describes the low-energy worldvolume dynamics of BPS domain walls in four-dimensional N=1 SYM theory. We demonstrate how to obtain the same theory in a brane configuration of type IIB string theory that contains threebranes and fivebranes. A combination of string and field theory techniques allows us to re-formulate some of the well-known properties of N=1 SYM domain walls in a geometric language and to postulate a Seiberg-like duality for the Acharya-Vafa theory. In the process, we obtain new information about the dynamics of branes in setups that preserve two supersymmetries. Using similar methods we also study other N=1 CS theories with extra matter in the adjoint and fundamental representations of the gauge group.Comment: 25 pages, 5 figure

Domain Walls in Supersymmetric Yang-Mills Theories

We present a detailed analysis of the domain walls in supersymmetric gluodynamics and SQCD. We use the (corrected) Veneziano-Yankielowicz effective Lagrangians to explicitely obtain the wall profiles and check recent results of Dvali and Shifman (Phys. Lett. B396, (1997) 64: (i) the BPS-saturated nature of the walls; (ii) the exact expressions for the wall energy density which depend only on global features of dynamics (the existence of a non-trivial central extension of N=1 superalgebra in the theories which admit wall-like solutions). If supersymmetry is softly broken by the gluino mass, the degeneracy of the distinct vacua is gone, and one can consider the decay rate of the "false" vacuum into the genuine one. We do this calculation in the limit of the small gluino mass. Finally, we comment on the controversy regarding the existence of $N$ distinct chirally asymmetric vacua in SU(N) SUSY gluodynamics.Comment: 26 pages, Latex, several misprints corrected, final version to be published in Phys.Rev.

The Center symmetry and its spontaneous breakdown at high temperatures

We examine the role of the center Z(N) of the gauge group SU(N) in gauge theories. In this pedagogical article, we discuss, among other topics, the center symmetry and confinement and deconfinement in gauge theories and associated finite-temperature phase transitions. We also look at universal properties of domain walls separating distinct confined and deconfined bulk phases, including a description of how QCD color-flux strings can end on color-neutral domain walls, and unusual finite-volume dependence in which quarks in deconfined bulk phase seem to be "confined".Comment: LaTex, 35 pages, 6 figures, uses sprocl.sty. To be published in the Festschrift in honor of B.L. Ioffe, "At the Frontier of Particle Physics/ Handbook of QCD", edited by M. Shifma

Skyrmions from Instantons inside Domain Walls

Some years ago, Atiyah and Manton described a method to construct approximate Skyrmion solutions from Yang-Mills instantons. Here we present a dynamical realization of this construction using domain walls in a five-dimensional gauge theory. The non-abelian gauge symmetry is broken in each vacuum but restored in the core of the domain wall, allowing instantons to nestle inside the wall. We show that the worldvolume dynamics of the wall is given by the Skyrme model, including the four-derivative term, and the instantons appear as Skyrmions.Comment: 11 pages, 1 figure. v1: References added. v2: typos correcte

Lattice Gauge Theories at the Energy Frontier

This White Paper has been prepared as a planning document for the Division of High Energy Physics of the U. S. Department of Energy. Recent progress in lattice-based studies of physics beyond the standard model is summarized, and major current goals of USQCD research in this area are presented. Challenges and opportunities associated with the recently discovered 126 GeV Higgs-like particle are highlighted. Computational resources needed for reaching important goals are described. The document was finalized on February 11, 2013 with references that are not aimed to be complete, or account for an accurate historical record of the field.Comment: Submitted for the Snowmass 2013 e-Proceedings with 44 pages, 10 figures, and 3 table