Resurgence theory implies that the non-perturbative (NP) and perturbative (P) data in a QFT are quantitatively related, and that detailed information about nonperturbative saddle point field configurations of path integrals can be extracted from perturbation theory. Traditionally, only stable NP saddle points are considered in QFT, and homotopy group considerations are used to classify them. However, in many QFTs the relevant homotopy groups are trivial, and even when they are non-trivial they leave many NP saddle points undetected. Resurgence provides a refined classification of NP-saddles, going beyond conventional topological considerations. To demonstrate some of these ideas, we study the SU(N ) principal chiral model (PCM), a two dimensional asymptotically free matrix field theory which has no instantons, because the relevant homotopy group is trivial. Adiabatic continuity is used to reach a weakly coupled regime where NP effects are calculable. We then use resurgence theory to uncover the existence and role of novel 'fracton' saddle points, which turn out to be the fractionalized constituents of previously observed unstable 'uniton' saddle points. The fractons play a crucial role in the physics of the PCM, and are responsible for the dynamically generated mass gap of the theory. Moreover, we show that the fracton-anti-fracton events are the weak coupling realization of 't Hooft's renormalons, and argue that the renormalon ambiguities are systematically cancelled in the semi-classical expansion. Our results motivate the conjecture that the semi-classical expansion of the path integral can be geometrized as a sum over Lefschetz thimbles.

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.

We show that the squared speed of sound v 2 s is bounded from above at high temperatures by the conformal value of 1/3 in a class of strongly coupled four-dimensional field theories, given some mild technical assumptions. This class consists of field theories that have gravity duals sourced by a single scalar field. There are no known examples to date of field theories with gravity duals for which v 2 s exceeds 1/3 in energetically favored configurations. We conjecture that v 2 s = 1/3 represents an upper bound for a broad class of four-dimensional theories.Introduction. The gauge/gravity duality, which relates gauge theories to string theories in higher-dimensional spaces [1], has been used in recent years to shed light on the properties of plasmas described by strongly coupled, large N c gauge theories. When a field theory that has a string dual is in the large N c and strong coupling limits, the string dual generally reduces to a classical supergravity theory. This allows one to get information on strongly coupled quantum gauge theories by doing classical calculations in higher-dimensional 'holographic' gravitational theories. For instance, transport coefficients, which are normally theoretically inaccessible in strongly coupled systems, can be calculated in theories with gravity duals.

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.

Bottom-up holographic models of QCD, inspired by the anti-de Sitter space/conformal field theory correspondence, have shown a remarkable degree of phenomenological success. However, they rely on a number of bold assumptions. We investigate the reliability of one of the key assumptions, which involves matching the parameters of these models to QCD at high 4D momentum q 2 and renormalization scale µ 2 . We show that this leads to phenomenological and theoretical inconsistencies for scale-dependent quantities such as qq .