Quantum Fields and Strings

We compute the scaling dimensions of a large class of disorder operators ("monopoles") in the planar limit of CS-fermion theories.  The lightest such operator is shown to have dimension (2/3) k^{3/2}, where k is the CS level.  The computation is based on recently developed techniques for solving CS-matter at all 't Hooft couplings, and the operator dimensions are obtained by finding complex saddles in the low-temperature phase of the CS-fermion path integral in a monopole background.  We will also discuss the implications of this result to 3D bosonization dualities.

We construct a new model of four-dimensional relativistic strings with integrable dynamics on the worldsheet. In addition to translational modes this model contains a single massless pseudoscalar worldsheet field - the worldsheet axion. The axion couples to a topological density which counts the self-intersection number of a string. The corresponding coupling is fixed by integrability to Q=716π−−−√≈0.37. We argue that this model is a member of a larger family of relativistic non-critical integrable string models. This family includes and extends conventional non-critical strings described by the linear dilaton CFT. Intriguingly, recent lattice data in SU(3) and SU(5) gluodynamics reveals the presence of a massive pseudoscalar axion on the worldsheet of confining flux tubes. The value of the corresponding coupling, as determined from the lattice data, is equal to QL≈0.38±0.04.

Some 5d gauge theories have a 6d N=(1,0) SCFT as their UV completion. Given such 5d gauge theory we desire to determine its 6d UV completion. In this talk, I will present a method to do this for 5d gauge theories that can be engineered in string theory by brane webs. This can then be applied to study compactification of 6d N=(1,0) SCFT's on a torus.

We consider 4d N=1 superconformal theories on a cylinder. The partition function on this geometry computes the superconformal index, and can be obtained via the path integral with time direction compactified on a circle and periodic conditions for fermions. We will describe universal formulas for the asymptotics of such partition functions in the limit of very large circle and of very small circle. These limits are completely fixed in terms of coefficients of the Weyl anomaly (a,c). We will explain why supersymmetry is a necessary condition in 4d to establish these higher dimensional analogues of classic results in 2d CFTs. Finally we will discuss some applications and the extension to 6d.

The gauged linear sigma model (GLSM) with (0,2) supersymmetry is an excellent tool for generating solutions of the heterotic string. In this talk, I will review a novel mechanism within the (0,2) GLSM for producing target spaces with H-flux, and explore several examples of this type. Along the way, a remarkable relationship between (0,2) gauge anomalies and H-flux will emerge. We will also see hints that many of these spaces require a stringy notion of geometry.

Quantum field theory on curved space has long been studied for its interesting phenomenology, and more recently also as a means to obtain non-perturbative results in supersymmetric theories. In this talk I will describe the holographic dual for N=4 SYM coupled to massive N=2 flavors on spaces of constant curvature. With that in hand, I will discuss a topology-changing phase transition on S^4 and confront holographic computations with exact field theory results obtained using supersymmetric localization.

We consider quantum quench from a gapped to a gapless system in 1+1 dimensions. We 

provide a rigorous proof of the thermalization of the reduced density matrix, hence that of

an arbitrary string of local operators in an interval. In case the system is integrable, the "thermalization" leads to a generalized Gibbs ensemble (GGE). We model the critical quench in terms of an initial state in terms of a conformal boundary state deformed by exponential cutoffs involving hamiltonian and other charges. We justify this choice of the initial state by explicitly

deriving it in free boson and free fermion systems with time-dependent mass. A surprising result we find is that for generic quenches and observables the higher charges remain 

important even if the initial gap is arbitrarily high, contrary to standard RG expectations.

( based on hep-th/1501.04580  and a couple of upcoming papers)

I will revisit the A-twisted gauged linear sigma model (GLSM) in the case of (2,2) supersymmetry in two dimensions, and its Omega-background deformation. Exact results for correlation functions on the sphere can be obtained in terms of Jeffrey-Kirwan residues on the Coulomb branch, which has a number of interesting applications. I will also explain an interesting generalization to (0,2) supersymmetric GLSMs of a special type.

I will describe entanglement entropy of a cap-like region for a generic quantum field theory residing in the Bunch-Davies vacuum on de Sitter space. Entanglement entropy in this setup is identical with the thermal entropy in the static patch of de Sitter, and it is possible to derive a simple relation between the vacuum expectation value of the energy-momentum tensor trace and the RG flow of entanglement entropy. In particular, renormalization of the cosmological constant and logarithmic divergence of the entanglement entropy are interrelated in this setup. These findings are confirmed by recovering known universal contributions for a free field theory deformed by a mass operator as well as correct universal behaviour at the fixed points. In three dimensions the renormalized entanglement entropy is stationary at the fixed points but not monotonic. Computational evidence that the universal `area law' for a conformally coupled scalar is different from the known result in the literature will be given, and I will argue that this difference survives in the limit of flat space.

In this talk I will discuss the most singular point and T^2 compactifications of a 6d N=(1,0) supersymmetric conformal field theory (SCFT) which arises as the worldvolume theory on coincident N of M5 branes probing the singular locus of the ALE orbifold. When N=1, the compactified theory can be describe by a class S theory of three punctured sphere. Generalization to multiple M5s case results in a pair of 4d N=2 SCFTs which are connected by a IR free gauge multiplet. Along the line, we see that the “dynamical version" of class S simple puncture plays a role. Closing one of two flavor groups, we can isolate one of them with manifest SL(2,Z) invariance of T^2 and a non-abelian flavor group, including presumably new N=2 SCFTs.

We derive the constitutive relations of first order charged hydrodynamics for theories with Lifshitz scaling and broken parity in 2+1 and 3+1 spacetime dimensions. In addition to the anomalous (in 3+1) or Hall (in 2+1) transport of relativistic hydrodynamics, there is an additional non-dissipative transport allowed by the absence of boost invariance. We analyze the non-relativistic limit and use a phenomenological model of a strange metal

to argue that these effects can be measured in principle by using electromagnetic fields with non-zero gradients.