We constructed all possible kinematically allowed three-point interactions of two massless Dirac spinors with massive higher-spin bosons. In any $\textit{D}$ spacetime, the interactions have been constructed using the projections of the higher spin irreducible representations of Spin($\textit{D}$ − 1) over the product of two irreducible spinor representations of Spin($\textit{D}$ − 2). Based on this analysis, we have further classified the space of theories involving two massless Dirac spinors and a single (or multiple) massive higher spin(s) based on the discrete symmetries: $\textit{C}$, $\textit{R}$, and $\textit{T}$. We found that in any $\textit{D}$ = 2$\textit{m}$ + 1/2$\textit{m}$, the interacting theories of a single massive higher spin have a “$\textit{m}$” mod 2 (or $\textit{D}$ mod 4) classification.

India

South Africa

Kushal Chakraborty

Aakash Kumar

Arnab Rudra

Germany

Amey Yeole

Three point interaction of Dirac fermions with higher spin particles and discrete symmetries

We use on-shell Supersymmetry to constrain the three-point function of two massless particles and one massive particle in 3+1 dimensions. We use this information to write down the tree-level four-point function of massless particles for   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1, 2 and 4 theories. In particular, we derive the expressions for four-photon/gluon amplitudes with massive higher spin exchange in theories with   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 Supersymmetry in 3+1 dimensions.

Mahesh Balasubramanian

Arnab Saha

On-shell supersymmetry and higher-spin amplitudes

Two derivative Jackiw-Teitelboim (JT) gravity theory captures the near-horizon dynamics of higher dimensional near-extremal black holes, which is governed by a Schwarzian action at the boundary in the near-horizon region. The partition function corresponding to this boundary action correctly gives the statistical entropy of the near-extremal black hole. In this paper, we study the thermodynamics of spherically symmetric four-dimensional near-extremal black holes in presence of arbitrary perturbative four derivative corrections. We find that the near-horizon dynamics is again captured by a JT-like action with a particular namely R 2 higher derivative modification. Effectively the theory is described by a boundary Schwarzian action which gets suitably modified due to the presence of the higher derivative interactions. Near-extremal entropy, free energy also get corrected accordingly.

Nabamita Banerjee

Taniya Mandal

Muktajyoti Saha

Equivalence of JT gravity and near-extremal black hole dynamics in higher derivative theory

We provide a systematic method to compute tree-level scattering amplitudes with spinning external states from amplitudes with scalar external states in arbitrary spacetime dimensions. We write down analytic answers for various scattering amplitudes, including the four graviton amplitude due to the massive spin J exchange. We verify the results by computing angular distributions in 3 + 1 dimensions using various identities involving Jacobi polynomials.

Raj Patil

Spinning amplitudes from scalar amplitudes

We show that the Atiyah-Patodi-Singer η-invariant can be related to the temperature-dependent Witten index of a noncompact theory and give a new proof of the APS theorem using scattering theory. We relate the η-invariant to a Callias index and compute it using localization of a supersymmetric path integral. We show that the η-invariant for the elliptic genus of a finite cigar is related to quantum modular forms obtained from the completion of a mock Jacobi form which we compute from the noncompact path integral.

France

Italy

Atish Dabholkar

Diksha Jain

APS η-invariant, path integrals, and mock modularity

We compute leading soft theorem for multiple gravitini (and gravitons) in an arbitrary theory of supergravity with an arbitrary number of finite energy particles by extending Sen’s approach [1, 2] to fermionic symmetry. Our results are independent of the mass and the spin of the external particles. Our results are valid for any compactification of type II and Heterotic superstring theory. Our results are valid at all orders in perturbation theory for four and higher spacetime dimensions.

Leading soft theorem for multiple gravitini

While the notion of open quantum systems is itself old, most of the existing studies deal with quantum mechanical systems rather than quantum field theories. After a brief review of field theoretical/path integral tools currently available to deal with open quantum field theories, we go on to apply these tools to an open version of ϕ 3 + ϕ 4 theory in four spacetime dimensions and demonstrate its one loop renormalizability (including the renormalizability of the Lindblad structure).

Avinash Baidya

Chandan Jana

R. Loganayagam

United States

Renormalization in open quantum field theory. Part I. Scalar field theory

We explore the Mellin representation of correlation functions in conformal field theories in the weak coupling regime. We provide a complete proof for a set of Feynman rules to write the Mellin amplitude for a general tree level Feynman diagram involving only scalar operators. We find a factorised form involving beta functions associated to the propagators, similar to tree level Feynman rules in momentum space for ordinary QFTs. We also briefly consider the case where a generic scalar perturbation of the free CFT breaks conformal invariance. Mellin space still has some utility and one can consider non-conformal Mellin representations. In this context, we find that the beta function corresponding to conformal propagator uplifts to a hypergeometric function.

Amin Nizami

Sourav Sarkar

Mritunjay Verma

Exploring perturbative conformal field theory in Mellin space

This paper investigates relationships between low-energy four-particle scattering amplitudes with external gauge particles and gravitons in the E 8 × E 8 and SO(32) heterotic string theories and the type I and type IA superstring theories by considering a variety of tree level and one-loop Feynman diagrams describing such amplitudes in eleven-dimensional supergravity in a Horava-Witten background compactified on a circle. This accounts for a number of perturbative and non-perturbative aspects of low order higher derivative terms in the low-energy expansion of string theory amplitudes, which are expected to be protected by half maximal supersymmetry from receiving corrections beyond one or two loops. It also suggests the manner in which type I/heterotic duality may be realised for certain higher derivative interactions that are not so obviously protected. For example, our considerations suggest that R 4 interactions (where R is the Riemann curvature) might receive no perturbative corrections beyond one loop by virtue of a conspiracy involving contributions from (non-BPS) ℤ 2 $$ {\mathbb{Z}}_2 $$ D-instantons in the type I and heterotic SO(32) theories.

United Kingdom

Michael Green

Type I/heterotic duality and M-theory amplitudes

In some string theories, e.g. SO(32) heterotic string theory on Calabi-Yau manifolds, a massless field with a tree level potential can acquire a tachyonic mass at the one loop level, forcing us to quantize the theory around a new background that is not a solution to the classical equations of motion and hence is not described by a conformally invariant world-sheet theory. We describe a systematic procedure for carrying out string perturbation theory around such backgrounds.