We compute the supersymmetric index of half BPS black holes in N=2 supergravity with higher curvature corrections and show that the result agrees with the degeneracy of supersymmetric extremal black holes carrying the same charges. Both sides of the computation are done gravitationally.

Germany

Subramanya Hegde

India

Ashoke Sen

P. Shanmugapriya

Amitabh Virmani

Supersymmetric index for half BPS black holes in N=2 supergravity with higher curvature corrections

We study on-shell functions in the kinematic space for the Coulomb branch of  $$\mathcal{N}$$  = 4 SYM. We construct BCFW bridges that help us build bigger on-shell functions. As a consequence, we provide on-shell diagram formulations for BCFW shifts that correspond to various mass configurations. We will use this to calculate the quadruple cut for the one-loop amplitude on the Coulomb branch and maximal cuts for higher-loops. We make preliminary comments on finding the inequivalent set of on-shell functions for the Coulomb branch.

Md. Abhishek

Dileep Jatkar

Arnab Saha

Amit Suthar

On-shell functions on the Coulomb branch of  $$\mathcal{N}$$  = 4 SYM

We discuss the construction of duality defects in c = 24 meromorphic CFTs that correspond to Niemeier lattices. We will illustrate our constructions for the D  n -type lattices. We will identify non-anomalous ℤ2 symmetries of these theories, and we show that on orbifolding with respect to these symmetries, these theories map to each other. We investigate this map, and in the case of self-dual orbifolds, we provide the duality defect partition functions. We show that exchange automorphisms in some CFTs give rise to a new class of defect partition functions.

Sachin Grover

Duality defects in D  n -type Niemeier lattice CFTs

We study four point planar loop amplitudes at an arbitrary point in the Coulomb branch of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 super-Yang-Mills theory. We study two particle unitary cuts up to four loop order. We explicitly verify that bubble and triangle graphs do not contribute at one loop level and show that the results hold at higher loop level as well. We also write down an all loop recursion relation for two particle reducible graphs for four point amplitudes.

Loop amplitudes in the Coulomb branch of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 super-Yang-Mills theory

In a recent paper [arXiv:2308.00038], Anupam, Chowdhury, and Sen conjectured that the finite temperature Euclidean five-dimensional Cvetic-Youm solution saturating the BPS bound is supersymmetric. In this paper, we explicitly construct Killing spinors for this solution in five-dimensional minimal supergravity. We also expand on the previous discussions of Killing spinors for the finite temperature Euclidean Kerr-Newman solution saturating the BPS bound. For both these cases, we show that the total charge gets divided into two harmonic sources on three-dimensional flat base space.

Killing spinors for finite temperature Euclidean solutions at the BPS bound

In this paper we use the superconformal approach to derive the higher derivative action for 𝒩 = 3 Poincaré supergravity in four space-time dimensions. We first study the coupling of 𝒩 = 3 vector multiplets to conformal supergravity. Thereafter we combine it with the pure 𝒩 = 3 conformal supergravity action and use a minimum of three vector multiplets as compensators to arrive at Poincaré supergravity with higher derivative corrections. We give a general prescription on how to eliminate the auxiliary fields in an iterative manner and obtain the supergravity action order by order in derivatives. We also show that the truncation of the action at fourth order in derivatives is a consistent truncation.

Madhu Mishra

Debangshu Mukherjee

Bindusar Sahoo

Higher derivative invariants in four dimensional 𝒩 = 3 Poincaré supergravity

In this paper we derive the action for N = 3 conformal supergravity in four space-time dimensions. We construct a density formula for N = 3 conformal supergravity based on the superform action principle. Finally, we embed the N = 3 Weyl multiplet in the density formula to obtain the invariant action for N = 3 conformal supergravity. There are two inequivalent embeddings by changing a particular coefficient from real to imaginary. They lead to invariant actions, which will either be the supersymmetrization of the Weyl square term or the Pontryagin density in the eventuality of gauge fixing to Poincaré supergravity. As a consistency check of our formalism, we will show that the supersymmetrization of the Pontryagin density is a total derivative. We will demonstrate this for purely bosonic terms. We will also present the complete action for the supersymmetrization of Weyl square term. We also discuss consistent truncation of N = 4 Weyl multiplet to N = 3 Weyl multiplet and use it for a robust check of our results using the earlier known results in N = 4 conformal supergravity.

N = 3 conformal supergravity in four dimensions

Generalised bi-adjoint scalar amplitudes, obtained from integrations over moduli space of punctured ℂℙ k − 1, are novel extensions of the CHY formalism. These amplitudes have realisations in terms of Grassmannian cluster algebras. Recently connections between one-loop integrands for bi-adjoint cubic scalar theory and   <math> <msub> <mi>D</mi> <mi>n</mi> </msub> </math>  $$ {\mathcal{D}}_n $$  cluster polytope have been established. In this paper using the Gr (3, 6) cluster algebra, we relate the singularities of (3, 6) amplitude to four-point one-loop integrand in the bi-adjoint cubic scalar theory through the   <math> <msub> <mi>D</mi> <mn>4</mn> </msub> </math>  $$ {\mathcal{D}}_4 $$  cluster polytope. We also study factorisation properties of the (3, 6) amplitude at various boundaries in the worldsheet.

One-loop integrand from generalised scattering equations

Superconformal matter multiplets play a crucial role in the construction of Poincaré supergravity invariants. Off-shell multiplets allow for construction of general matter couplings in supergravity. In [P. S. Howe, K. S. Stelle, and P. K. Townsend, Nucl. Phys. B214, 519 (1983)], relaxed hypermultiplet was constructed in rigid supersymmetry which on coupling with the real scalar multiplet allowed for an off-shell formulation of the rigid hypermultiplet. In this paper, we extend the relaxed hypermultiplet to conformal supergravity. For consistency with the superconformal algebra, we find that the fields have to be allowed to transform in a noncanonical way under <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo></math> <math><mi>R</mi></math>-symmetry. We find suitable field redefinitions to obtain fields which are irreducible representations of <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo></math> <math><mi>R</mi></math>-symmetry and present the full nonlinear transformation rule.

Aravindhan Srinivasan

Relaxed hypermultiplet in four dimensional <math><mi>N</mi><mo>=</mo><mn>2</mn></math> conformal supergravity

We will use the covariant superform approach to develop a new density formula for     <math> <mi>N</mi> </math> $$ \mathcal{N} $$  = 2 conformal supergravity which is based on a fermionic multiplet whose lowest component is a dimension-5/2 spinor. We will show that this density formula admits an embedding of the real scalar multiplet of [1]. Upon using the embedding of the tensor multiplet into the real scalar multiplet, we will construct a new higher derivative action of the tensor multiplet in     <math> <mi>N</mi> </math> $$ \mathcal{N} $$  = 2 conformal supergravity.