Quantum Fields and Strings

Quantum complexity is conjectured to probe inside of black hole horizons (or wormhole) via gauge gravity correspondence. In order to have a better understanding of this correspondence, we study time evolutions of complexities for generic Abelian pure gauge theories. For this purpose, we discretize U(1) gauge group as Z_N and also continuum spacetime as lattice spacetime, and this enables us to define a universal gate set for these gauge theories, and evaluate time evolutions of the complexities explicitly. We find that to achieve a large complexity ∼exp(entropy), which is one of the conjectured criteria necessary to have a dual  black hole, the Abelian gauge theory needs to be maximally nonlocal. (Based on collaboration with Norihiro Iizuka and Sotaro Sugishita, https://arxiv.org/abs/1707.03840)

We study the boundary conditions in the topologically twisted Chern-Simons matter theories with the Lie 3-algebraic structure. We find that the supersymmetric boundary conditions and the gauge invariant boundary conditions can be unified as the complexified gauge invariant boundary conditions which lead to the supergroup WZW models. We examine the BPS indices of the supergroup WZW models which may describe certain junctions of M2-branes and M5-branes by identifying the vacuum configurations of the brane system with the weight diagrams of the associated Lie superalgebras. For the case arising from the BLG model an explicit expression can be given in terms of a mock modular form. We will also consider the alternative matrix quantum mechanical descriptions of the supergroup WZW models. The talk will be based on recent works arXiv:1512.06646, arXiv:1612.07565 and ongoing research.

We will discuss some expectations regarding properties of N=1 SCFTs in four dimensions obtained by compactifying (1,0) theories in six dimensions on a Riemann surface. We will illustrate in detail how these properties come about in the special case of compactifications of two M5 branes probing Z_2 singularity.  In particular, we will obtain a large class of strongly coupled  N=1 theories in four dimensions obtained in such compactifications. We will derive some of their robust properties, such as anomalies and supersymmetric indices.

The AdS/Ricci-flat (AdS/RF) correspondence is a map between families of asymptotically locally AdS solutions on a torus and families of asymptotically flat spacetimes on a sphere. In this talk I will discuss how to relax these restrictions for linearized perturbations around solutions connected via the original AdS/RF correspondence.
To this end we perform a Kaluza-Klein (KK)  reduction, keeping all (massive) KK modes,  of AdS on torus and of Minkowski on a sphere.  We show that in the limit of large dimension of the compact manifolds (torus and sphere), the AdS/RF correspondence maps individual KK modes from one side to the other.
When the dimension is finite, the correspondence maps single modes to infinite superpositions of modes. One may further take appropriate limits so that there is either no torus (AdS side) or no sphere (Minkowski side) to map perturbations of solutions that possess no symmetry, thus completely relaxing the original restrictions.
This correspondence should allow us to develop a detailed holographic dictionary for asymptotically flat spacetimes.

I discuss a string theoretic approach to integrable lattice models. This approach provides a unified perspective on various important notions in lattice models, and relates these notions to four-dimensional N = 1 supersymmetric field theories and their surface operators.  I explain how my construction connects to Costello's work and the Nekrasov-Shatashvili correspondence.

The properties of physical processes reflect themselves in the structure of the relevant observables. This idea has been largely exploited for the flat space  S-matrix, whose analytic structure is determined by locality and unitary, the two pillars which our current understanding of nature is based on. In this context, it  has been possible to find new mathematical structures whose properties turn out to be the ones we ascribe to scattering processes in flat-space, so that both  unitarity and locality can be viewed as emergent from some more fundamental structure. However, the S-matrix does certainly not exhaust all the physical information contained in a theory and thus an interesting question to ask is whether and how we can get a similar and deeper understanding of other observables.

In this talk I will report on some recent progress towards such a formulation for quantities such as the universe wave-function and late-time correlators. In particular, I will focus on the perturbative representations of such quantities, their analytic properties and their geometrical interpretation as volumes of certain new polytopes. I  will consider a specific toy model which allows to extend most of the discussion to other set-ups than the cosmological one, such as flat and AdS space-times.

The talk will review the computation of the three point function of gauge-invariant operators in the planar N=4 SYM theory using integrability-based methods. The structure constant can be decomposed, as proposed by Basso, Komatsu and Vieira, in terms of two form-factor-like objects (hexagons). The multiple sums and integrals implied by the hexagon decomposition can be performed in the large-charge limit, and be compared to the results obtained by semiclassics. I will discuss a method to perform these sums and the contributions currently accessible by this approach.

I will introduce the spectral function method in the context of conformal bootstrap. I will discuss some applications of this method in two dimensions: (1) substantial evidence for the conjecture that the only unitary c>1 CFT with Virasoro primaries of bounded spin is Liouville theory, (2) detailed modular constraints on the spectrum of small c CFTs, (3) spectral density of large c CFTs with large gap, in connection to the (non-)universality of BTZ black hole entropy.

I will discuss the chiral algebra W_infty which is obtained from the Virasoro algebra by adding fields of spin 3, 4, .... Via a non-local non-linear map one can show that it is equivalent to Tsymbaliuk's Yangian of affine u(1). In this way we find an infinite number of commuting conserved charges. Diagonalizing these, the representation theory reduces to combinatorial study of plane partitions, 3-dimensional generalization of the Young diagrams. Tsymbaliuk's presentation can be derived from RTT relations using Maulik-Okounkov's free boson R-matrix.

Recently a boundary energy-momentum tensor Tzz has been constructed from the soft graviton operator for any 4D quantum theory of gravity in asymptotically flat space. Up to an "anomaly" which is one-loop exact, Tzz generates a Virasoro action on the 2D celestial sphere at null infinity. Here we show by explicit construction that the effects of the IR divergent part of the anomaly can be eliminated by a one-loop renormalization that shifts Tzz.