High Energy Physics

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.

Any quantum field theory can be thought of as arising from a perturbed UV conformal field theory, suggesting that information about the full RG flow is encoded in the original CFT. I will discuss ongoing work developing new methods for extracting this information to study strongly-coupled IR dynamics. This method uses a UV basis of conformal Casimir eigenstates to construct the Hamiltonian, which is then truncated at some maximum Casimir eigenvalue and diagonalized to approximate the low energy spectrum of the IR theory. After presenting a general framework which can be applied to CFTs in any number of dimensions, I will then focus on the specific example of scalar field theory, which can be used to study strongly-coupled systems like the 2D and 3D Ising models. Finally, I will discuss the possible application of this framework to gauge theories, including QCD.

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.

In the framework of the ordinary seesaw model with right-handed neutrinos (and nothing else) we show that the total lepton number violating decay of the Higgs doublet into a right-handed neutrino and a standard model lepton can successfully account for the baryon asymmetry of the Universe. This is possible thanks to thermal effects shortly before the sphalerons decouple.

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.

We derive in the framework of soft collinear effective field theory (SCET) a Lagrangian describing the t-channel exchange of Glauber quarks, which are incorporated through fermionic potential operators in the effective theory. The Wilson line structure of the operators, which is derived from matching calculations and the symmetries of the effective theory, describe additional soft and collinear emissions from a fermionic t-channel exchange in the forward scattering limit to all orders. Lightcone singularities in the fermionic potential are regulated using a rapidity regulator, whose corresponding renormalization group evolution gives rise to the quark reggeization at amplitude level.

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.