Order Parameters and Color-Flavor Center Symmetry in QCD.

Common lore suggests that N-color QCD with massive quarks has no useful order parameters that can be nontrivial at zero baryon density. However, such order parameters do exist when there are n_{f} quark flavors with a common mass and d≡gcd(n_{f},N)>1. These theories have a Z_{d} color-flavor center symmetry arising from intertwined color center transformations and cyclic flavor permutations. The symmetry realization depends on the temperature, baryon chemical potential, and value of n_{f}/N, with implications for conformal window studies and dense quark matter.

Chiral Lagrangian from Duality and Monopole Operators in Compactified QCD.

We show that there exists a special compactification of QCD on R^{3}×S^{1} in which the theory has a domain where continuous chiral symmetry breaking is analytically calculable. We give a microscopic derivation of the chiral Lagrangian, the chiral condensate, and the Gell-Mann-Oakes-Renner relation m_{π}^{2}f_{π}^{2}=-m_{q}⟨q[over ¯]q⟩. Abelian duality, monopole operators, and flavor-twisted boundary conditions play the main roles. The flavor twisting leads to the new effect of fractional jumping of fermion zero modes among monopole instantons. Chiral symmetry breaking is induced by monopole-instanton operators, and the Nambu-Goldstone pions arise by color-flavor transmutation from gapless "dual photons." We also give a microscopic picture of the "constituent quark" masses. Our results are consistent with expectations from chiral perturbation theory at large S^{1}, and yield strong support for adiabatic continuity between the small-S^{1} and large-S^{1} regimes. We also find concrete microscopic connections between N=1 and N=2 supersymmetric gauge theory dynamics and nonsupersymmetric QCD dynamics.

Casimir Energy of Confining Large N Gauge Theories.

Four-dimensional asymptotically free large N gauge theories compactified on S(R)(3)×R have a weakly coupled confining regime when R is small compared to the strong scale. We compute the vacuum energy of a variety of confining large N nonsupersymmetric gauge theories in this calculable regime, where the vacuum energy can be thought of as the S(3) Casimir energy. The N=∞ renormalized vacuum energy turns out to vanish in the class of theories we have examined. This matches an implication of a recently observed temperature-reflection symmetry of such systems.

Resurgence in quantum field theory: nonperturbative effects in the principal chiral model.

We explain the physical role of nonperturbative saddle points of path integrals in theories without instantons, using the example of the asymptotically free two-dimensional principal chiral model (PCM). Standard topological arguments based on homotopy considerations suggest no role for nonperturbative saddles in such theories. However, the resurgence theory, which unifies perturbative and nonperturbative physics, predicts the existence of several types of nonperturbative saddles associated with features of the large-order structure of the perturbation theory. These points are illustrated in the PCM, where we find new nonperturbative "fracton" saddle point field configurations, and suggest a quantum interpretation of previously discovered "uniton" unstable classical solutions. The fractons lead to a semiclassical realization of IR renormalons in the circle-compactified theory and yield the microscopic mechanism of the mass gap of the PCM.

Volume independence in the large N limit and an emergent fermionic symmetry.

Large-N volume independence in circle-compactified QCD with adjoint Weyl fermions implies the absence of any phase transitions as the radius is dialed to arbitrarily small values. This class of theories is believed to possess a Hagedorn density of hadronic states. It turns out that these properties are in apparent tension with each other, because a Hagedorn density of states typically implies a phase transition at some finite radius. This tension is resolved if there are degeneracies between the spectra of bosonic and fermionic states, as happens in the N(f) = 1 supersymmetric case. Resolution of the tension for N(f) >1 then suggests the emergence of a fermionic symmetry at large N, where there is no supersymmetry. We can escape the Coleman-Mandula theorem since the N = ∞ theory is free, with a trivial S matrix. We show an example of such a spectral degeneracy in a nonsupersymmetric toy example which has a Hagedorn spectrum.

Orbifold equivalence and the sign problem at finite baryon density.

We point out that SO(2N(c)) gauge theory with N(f) fundamental Dirac fermions does not have a sign problem at finite baryon number chemical potential µ(B). One can thus use lattice Monte Carlo simulations to study this theory at finite density. The absence of a sign problem in the SO(2N(c)) theory is particularly interesting because a wide class of observables in the SO(2N(c)) theory coincide with observables in QCD in the large N(c) limit, as we show using the technique of large N(c) orbifold equivalence. We argue that the orbifold equivalence between the two theories continues to hold at finite µ(B) provided one adds appropriate deformation terms to the SO(2N(c)) theory. This opens up the prospect of learning about QCD at finite µ(B) using lattice studies of the SO(2N(c)) theory.

Model independent tests of Skyrmions and their holographic cousins.

We describe a new exact relation for large Nc QCD for the long-distance behavior of baryon form factors in the chiral limit. This model-independent relation is used to test the consistency of the structure of several baryon models. All 4D semiclassical chiral soliton models satisfy the relation, as does the Pomarol-Wulzer holographic model of baryons as 5D Skyrmions. However, remarkably, we find that the holographic model treating baryons as instantons in the Sakai-Sugimoto model does not satisfy the relation.