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Subramanya Hegde

Publications and source records attributed to Subramanya Hegde.

At least 19 recordsLinked to original sources
arXiv2026

Only Flat Spacetime is Full BPS in Four Dimensional N=3 and N=4 Supergravity

We investigate the fully supersymmetric solutions in a class of N=3 and N=4 higher derivative Poincaré supergravity theories. These class of theories are obtained within the framework of conformal supergravity using the standard Weyl multiplet and contains a set of terms related to the Weyl square term by supersymmetry. We work in the superconformal formalism and show that flat spacetime is the only fully supersymmetric solution in these theories. However, in N=2 Poincaré supergravity theories that falls into the same class, two fully supersymmetric stationary solutions exist: Bertotti-Robinson geometry ($AdS_2\times S^2$) and flat spacetime, which are known in the literature. We discuss the reason behind the richer vacua in N=2 supergravity compared to its N=3 and N=4 cousins.

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arXiv2025

Symplectic Grassmannian description of the Coulomb branch three and four point amplitudes

We present a formulation of the three- and four-point amplitudes on the Coulomb branch of N=4 SYM as integrals over the symplectic Grassmannian. We demonstrate that their kinematic spaces are equivalent to symplectic Grassmannians SpGr(n,2n). For the three-point case, we express the amplitude as an integral over the symplectic Grassmannian in a specific little group frame. In the four-point case, we show that the integral yields the amplitude up to a known kinematic factor. Building on the four-dimensional analysis, we also express the six-dimensional N = (1,1) SYM amplitude in terms of four-dimensional variables in a form that makes its symplectic Grassmannian structure manifest.

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arXiv2024

Differential Representation for Carrollian Correlators

The differential representation of AdS correlators offers a framework to express exchange Witten diagrams as functions of non-local differential operators applied to contact Witten diagrams. In this paper, we develop the differential representation for scalar Carrollian correlators. We first construct this representation using the recently formulated Carrollian limit of AdS Witten diagrams. We then provide an alternate intrinsic analysis that leverages the properties of the Carrollian bulk-to-boundary propagator. Using the differential representation, we also obtain differential Bern-Carrasco-Johansson (BCJ) relations for Carrollian correlators.

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arXiv2024

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

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.

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arXiv2024

Duality defects in $D_n$-type Niemeier lattice CFTs

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 $\mathbb{Z}_2$ 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.

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arXiv2024

Loop Amplitudes in the Coulomb Branch of $\mathcal{N}=4$ Super-Yang-Mills Theory

We study four point planar loop amplitudes at an arbitrary point in the Coulomb branch of $\mathcal{N}=4$ 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.

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arXiv2024

Killing Spinors for Finite Temperature Euclidean Solutions at the BPS Bound

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.

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arXiv2023

Higher derivative invariants in four dimensional N=3 Poincare supergravity

In this paper, we use the superconformal approach to derive the higher derivative action for N = 3 Poincare 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 Poincare 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.

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arXiv2022

N = 3 Conformal Supergravity in Four Dimensions

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 super form 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 the 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.

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arXiv2022

Defect Partition Function from TDLs in Commutant Pairs

We study topological defect lines in two character rational conformal field theories. Among them one set of two character theories are commutant pairs in $E_{8,1}$ conformal field theory. Using these defect lines we construct defect partition function in the $E_8$ theory. We find that the defects preserve only a part of the $E_8$ current algebra symmetry. We also determine the defect partition function in $c=24$ CFTs using these defects lines of 2 character theories and we find that, with appropriate choice of commutant pairs, these defects preserve all current algebra symmetries of c = 24 CFTs.

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arXiv2022

Scattering Amplitudes and BCFW in $\mathcal{N}=2^{\ast}$ Theory

We use massive spinor helicity formalism to study scattering amplitudes in $\mathcal{N}=2^*$ super-Yang-Mills theory in four dimensions. We compute the amplitudes at an arbitrary point in the Coulomb branch of this theory. We compute amplitudes using projection from $\mathcal{N}=4$ theory and write three point amplitudes in a convenient form using special kinematics. We then compute four point amplitudes by carrying out massive BCFW shifts of the amplitudes. We find some of the shifted amplitudes have a pole at $z=\infty$. Taking the residue at $z=\infty$ into account ensures little group covariance of the final result.

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arXiv2021

One-loop integrand from generalised scattering equations

Generalised bi-adjoint scalar amplitudes, obtained from integrations over moduli space of punctured $\mathbb{CP}^{k-1}$, 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 $\mathcal{D}_n$ cluster polytope have been established. In this paper using the $\text{Gr}\left(3,6\right)$ cluster algebra, we relate the singularities of $\left(3,6\right)$ amplitude to four-point one-loop integrand in the bi-adjoint cubic scalar theory through the $\mathcal{D}_{4}$ cluster polytope. We also study factorisation properties of the $(3,6)$ amplitude at various boundaries in the worldsheet.

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arXiv2021

Double Soft Theorem for Generalised Biadjoint Scalar Amplitudes

We study double soft theorem for the generalised biadjoint scalar field theory whose amplitudes are computed in terms of punctures on $\mathbb{CP}^{k-1}$. We find that whenever the double soft limit does not decouple into a product of single soft factors, the leading contributions to the double soft theorems come from the degenerate solutions, otherwise the non degenerate solutions dominate. Our analysis uses the regular solutions to the scattering equations. Most of the results are presented for $k=3$ but we show how they generalise to arbitrary $k$. We have explicit analytic results, for any $k$, in the case when soft external states are adjacent.

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arXiv2020

Relaxed hypermultiplet in four dimensional N=2 conformal supergravity

Superconformal matter multiplets play a crucial role in the construction of Poincare supergravity invariants. Off-shell multiplets allow for construction of general matter couplings in supergravity. In Nucl. Phys. B214 (1983) 519-531, 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 non-canonical way under SU(2) symmetry. We find suitable field redefinitions to obtain fields which are irreducible representations of SU(2) R-symmetry and present the full non-linear transformation rule.

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arXiv2019

New higher derivative action for tensor multiplet in N=2 conformal supergravity in four dimensions

We will use the covariant superform approach to develop a new density formula for $\mathcal{N}=2$ 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 [arXiv:1712.02309]. 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 $\mathcal{N}=2$ conformal supergravity.

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arXiv2018

Comment on "The N = 3 Weyl Multiplet in Four Dimensions"

N = 3 Weyl multiplet in four dimensions was first constructed in J van Muiden et al (2017) where the authors used the current multiplet approach to obtain the linearized transformation rules and completed the nonlinear variations using the superconformal algebra. The multiplet of currents was obtained by a truncation of the multiplet of currents for the N = 4 vector multiplet. While the procedure seems to be correct, the result suffers from several inconsistencies. The inconsistencies are observed in the transformation rules as well as the field dependent structure constants in the corresponding soft algebra. We take a different approach, and compute the transformation rule as well as the corresponding soft algebra by demanding consistency.

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arXiv2018

A 24+24 real scalar multiplet in four dimensional N=2 conformal supergravity

Starting from the 48+48 component multiplet of supercurrents for a rigid N=2 tensor multiplet in four spacetime dimensions, we obtain the transformation of the linearized supergravity multiplet which couples to this supercurrent multiplet. At the linearized level, this 48+48 component supergravity multiplet decouples into the 24+24 component linearized standard Weyl multiplet and a 24+24 component irreducible matter multiplet containing a real scalar field. By a consistent application of the supersymmetry algebra with field dependent structure constants appropriate to N=2 conformal supergravity, we find the full transformation law for this multiplet in a conformal supergravity background. By performing a field redefinition and switching off the conformal supergravity background, the multiplet is equivalent to the one introduced by Howe et al in flat space as a constrained real scalar superfield. We present a set of constraints which can be consistently imposed on this multiplet to obtain a restricted minimal 8+8 off-shell matter multiplet. We also show as an example the precise embedding of the tensor multiplet inside this multiplet.

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