Quantum Fields and Strings

I will discuss the conditions satisfied by the 2 → 2 scattering amplitude in unitarity and causal theories, presenting a simple formulation in term of moments of a positive measure. I will identify complete subsets of two-sided constraints, suitable to bound Effective Field Theories (EFTs) at any finite order in the energy expansion. I will also discuss  the importance of IR loop effects on these bounds. A consequence of this study is that EFTs in which the scattering amplitude in some regime grows in energy faster than E6 (e.g. higher spin particles with masses smaller than their inverse size) cannot be UV-completed.

We will describe an approach to the theory of fundamental particlesbased on finite-dimensional quantum algebras of observables. We will explain why the unimodularity of the color group suggests an interpretation of the quarklepton symmetry which involves the octonions and leads to the quantum spaces underlying the Jordan algebras of octonionic hermitian 2 × 2 and 3 × 3 matrices as internal geometry for fundamental particles. In the course of this talk, we will remind shortly why the finite-dimensional algebras of observables are the finite-dimensional euclidean Jordan agebras and we will describe their classifications. We will also explain our differential calculus on Jordan algebras and the theory of connections on Jordan modules. It is pointed out that the above theory of connections implies potentially a lot of scalar particles.

I will review recent progress in application of separation of variables method.

In particular I will review the construction for the integrable spin chains with gl(N) symmetry. 

By finding, for the first time, the matrix elements of the SoV measure explicitly I will show how to compute various correlation functions and wave function overlaps in a simple determinant form. 

General philosophy of application of these methods to the problems related to AdS/CFT, N=4 SYM etc. will be discussed too. 

The talk will focus on the spectrum of near-extremal black holes in gravity and near-BPS black holes in supergravity. For concreteness, we will study cases in asymptotically four-dimensional flat space and three-dimensional Anti-de Sitter. This will be done by analyzing quantum effects near the horizon captured by an emergent Jackiw-Teitelboim mode at low temperatures. This will allow us to systematically study questions such as the extremal degeneracy and the size of the gap in the black hole spectrum, which can be compared to some string theory constructions.

How to deal with diffeomorphism symmetries is one of the difficult problems in general relativity. Because of the diffeomorphism symmetries, we need to consider diffeomorphism invariant operators and gravitational dressing. In this work, we consider a special gravitational dressing which is to locate the operator by shooting geodesic from the spatial boundary. We try to use Peierls bracket to study the commutator between this gravitational dressing operator and the ADM energy operator. We found the ADM energy increase/decrease when the extra created out-going particle is in front of/behind the event horizon. Our result strengthens the Marolf-Polchinski firewall argument in some sense. In the talk, I will first briefly review the Peierls bracket, which is a linear response interpretation of bracket computation in covariant phase space formalism. We also illustrate the Peierls bracket with several examples. After that, we use Peierls bracket to study the Hamiltonian flow of the gravitational dressing operator, from which we can read out the commutator between the gravitational dressing operator with the ADM energy operator.

In this talk I will discuss the universal properties of thermal transport in conformal field theories that are perturbed by a TTbar operator. TTbar-deformation is known to be an exactly solvable deformation in that the spectrum of the undeformed theory alone suffices to predict that of the deformed theory. Unique properties of TTbar deformation allow us to study the TTbar-deformed CFTs using two disparate methods: integrability and holography. I will apply these two approaches to study the non-equilibrium steady states and Drude weights, finding perfect agreement. I will also explain how the integrability-based approach yields the exact momentum diffusion constant, which, to our surprise, also happens to satisfy a universal formula. Finally I will briefly touch upon a curious connection between TTbar-deformed CFTs and an integrable cellular automaton model called the Rule 54 chain.

The Ryu Takayanagi formula identifies the area of  extremal surfaces in AdS with the entanglement entropy of the boundary CFT. However the bulk microstate interpretation of the extremal area remains mysterious. Progress along this direction requires understanding how to define entanglement entropy in the bulk closed string theory. As a toy model for AdS/CFT, we study the entanglement entropy of closed strings in the topological A model in the context of Gopakumar Vafa duality. We give a self consistent factorization of the closed string Hilbert space which leads to string edge modes transforming under a q-deformed surface symmetry group. Compatibility with this symmetry requires a q-deformed definition of entanglement entropy. Using the topological vertex formalism, we define the Hartle Hawking state for the resolved conifold and compute its q-deformed entropy directly from the closed string reduced density matrix.  We show that this is the same as the generalized entropy, defined by prescribing a contractible replica manifold for the closed string theory on the resolved conifold.  We then apply the Gopakumar Vafa duality to reproduce the closed string entropy from Chern Simons dual  using the un-deformed definition of entanglement entropy. Finally we relate non local aspects of our factorization map to analogous phenomenon recently found in JT gravity.

Dilaton-gravity models are integrable in two dimensions and admit a holographic description. In this talk, the holographic description of the Dilaton-gravity in flat spacetime is discussed. Using the gauge theory formulation of the model we obtain the boundary action which under certain boundary conditions is of the Warped-Schwarzian type. We calculate the 1-loop partition function of the model as the coadjoint orbit of the warped Virasoro group.

I will review the numerical approach to testing gauge/gravity duality using matrix models. This will lead to a summary of recent results from the BFSS, BMN and Berkooz-Douglas matrix models and a strong non-perturbative test of gauge/gravity duality.