Quantum Fields and Strings

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.

I will discuss the Higgs-branch CFT2 dual to string theory on AdS3 x S3 x T4. States localised near the small instanton singularity can be described in terms of vector multiplet variables.  This theory has a planar, weak-coupling limit, in which anomalous dimensions of single-trace composite operators can be calculated. At one loop, the calculation reduces to finding the spectrum of a spin chain with nearest-neighbour interactions. This CFT2 spin chain matches precisely the one that was previously found as the weak-coupling limit of the integrable system describing the AdS3 side of the duality.  In particual I will show that the one-loop dilatation operator in a non-trivial compact subsector corresponds to an integrable spin-chain Hamiltonian. This provides the first direct evidence of integrability on the CFT2 side of the correspondence.

 

String theory is starting to provide novel all-loop precision tools for the computation of scattering amplitudes in the high energy (HE) limit of N=4 SYM theory. After a review of some key insights and results for hexagon amplitudes, I will describe ongoing developments addressing higher numbers of external gluons.