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My research spans three broad areas within theoretical high-energy physics: scattering amplitudes, supergravity, and conformal field theory. As is often the case in modern theoretical physics, these subjects are deeply interconnected. A recurring theme throughout my work is the role of symmetry in quantum field theory and gravity, which I study using tools drawn from these different frameworks.
Notional visualization of the amplituhedron. Source: Wikipedia
Scattering Amplitudes:
Our best description of nature (not including gravity at small distances) is quantum field theory. One of the defining features of quantum theory is that it predicts probabilities for physical processes rather than definite outcomes. In quantum field theory, one often calculates scattering amplitudes, from which the probabilities of scattering events can be determined. For eg, in the Large Hadron Collider (LHC), one collides protons, and as a result of their collision, various particles emerge. By studying the particles produced in such collisions, scattering experiments allow us to probe nature at the shortest accessible distance scales.
The traditional method to calculate scattering amplitudes in quantum field theory is by the use of Feynman diagrams. However, in the last couple of decades, there has been a revolution in finding novel ways to calculate amplitudes based on their fundamental properties rather than from Feynman diagrams. These methods go by the name of "On-shell methods" or "Unitarity-based methods".
The framework of quantum field theory involves notions such as 'virtual particles' that form the internal lines of a Feynman diagram. Modern amplitude methods rely on considering the limit when these virtual particles are made physical ("on-shell"). The scattering process then factorises into multiple scattering processes involving fewer external particles than the original process. This can be utilised to build recursive methods to compute scattering amplitudes.
The fact that scattering amplitudes lend themselves to these simpler and more efficient methods is surprising. Moreover, they have also been found to exhibit hidden symmetries not evident from the definition of the theory or from Feynman diagrams. To explain these rich and surprising mathematical structures of scattering amplitudes, a new framework of 'positive geometry' has emerged, where one strives to define scattering amplitudes in a manner that manifests all of their rich properties. It is an ambitious program that tries to reformulate the rules of perturbative quantum field theory by asking the basic question, "What is the question in kinematic space to which the scattering amplitude is the answer?"
My recent research focuses on the relationship between scattering amplitudes in massive theories—particularly the Coulomb branch of N=4 super Yang–Mills theory—and positive geometry. Amplitudes in this theory provide a natural testing ground for extending powerful on-shell methods beyond the massless setting. A central goal of my work is to investigate whether these amplitudes admit an amplituhedron-like positive-geometric description.
Key publications:
"Symplectic Grassmannian description of the Coulomb branch three and four point amplitudes” V. C. Cortes, Y. El Maazouz, S.H & A. Suthar. JHEP 12 (2025) 073 [arXiv:2505.03705 [hep-th]].
”On-shell functions on the Coulomb branch of N = 4 SYM” Md. Abhishek, S.H, D. P. Jatkar, A. P. Saha & A. Suthar. JHEP 05 (2024) 157 [arXiv:2311.17763 [hep-th]].
"Loop Amplitudes in the Coulomb Branch of N = 4 Super-Yang-Mills Theory” Md. Abhishek, S.H, D. P. Jatkar, A. P. Saha & A. Suthar. JHEP 03 (2024) 143 [arXiv:2308.05705 [hep-th]]
One-loop integrand from generalised scattering equations” Md. Abhishek, S.H, & A. P. Saha. JHEP 05 (2021) 012. [arXiv:2012.10916 [hep-th]].
An image of a black hole captured by the Event Horizon Telescope. For my work, black hole solutions act as a theoretical laboratory to test theories of quantum gravity. Source: Wikipedia
Supergravity:
Superstring theory is one of the leading candidates for a quantum theory of gravity. Unlike conventional attempts to quantise gravity as a quantum field theory, it is expected to avoid the ultraviolet infinities that arise at very short distances. At energies much lower than the string scale, superstring theory is described by supergravity, an effective theory containing the graviton together with its supersymmetric partners and other matter fields.
Supergravity provides a rich framework to explore the interplay between gravity, quantum field theory and symmetry. Besides being the low-energy limit of superstring theory, it has found numerous applications in topics ranging from black-hole physics to the AdS/CFT correspondence. Many of the quantitative tests of string theory, including the microscopic understanding of black-hole entropy, rely on a detailed understanding of the corresponding supergravity theories.
Constructing supergravity theories, however, is a technically challenging task. An elegant framework known as the superconformal tensor calculus simplifies this construction by first enlarging the symmetry of the theory and then systematically reducing it to the desired supergravity. This approach is particularly powerful for constructing higher-derivative corrections to supergravity actions, which play an important role in precision tests of string theory and in understanding quantum corrections to black-hole physics.
My research focuses on the construction of supergravity theories using superconformal methods, the study of their supersymmetric solutions, and their applications to black-hole physics. In particular, I am interested in higher-derivative supergravities and in understanding how their predictions precisely match microscopic results obtained from superstring theory.
Key publications:
Supersymmetric Index for Half BPS Black Holes in N=2 Supergravity with Higher Curvature Corrections” S.H, A. Sen, P. Shanmugapriya & A. Virmani. JHEP 02 (2025) 131 [arXiv:2411.08260 [hep-th]].
”Killing Spinors for Finite Temperature Euclidean Solutions at the BPS Bound” S.H, & A. Virmani. JHEP 02 (2024) 203 [arXiv:2311.09427 [hep-th]].
"N=2 dilaton Weyl multiplet in 4D supergravity" D. Butter, S.H, I. Lodato & B. Sahoo. JHEP 154, 03 (2018); [arXiv:1712.05365 [hep-th]].
Conformal Field Theory:
Conformal field theories (CFTs) are quantum field theories with an enhanced spacetime symmetry known as conformal symmetry. Their high degree of symmetry makes many physical quantities exactly calculable, making them indispensable laboratories for understanding strongly interacting quantum field theories. CFTs also play a central role in modern theoretical physics through their connections to critical phenomena, string theory, and the AdS/CFT correspondence.
One of the exciting recent developments in the study of conformal field theories is the emergence of generalised symmetries and topological defects. Unlike ordinary symmetries, which are associated with conserved charges, these extended symmetry structures provide a richer framework for classifying quantum field theories and understanding dualities between seemingly different physical systems. They have become an active area of research at the interface of quantum field theory, mathematics, and condensed matter physics.
My work in this area focuses on the study of topological defects and their applications in conformal field theories. In particular, I have investigated how defects encode symmetry information and can be used to construct and analyse new observables in conformal field theories.
Key publications:
"Duality defects in D_n-type Niemeier lattice CFTs” S. Grover, S.H & D. P. Jatkar. JHEP 05 (2024) 057 [arXiv:2312.17165 [hep-th]].
"Defect Partition Function from TDLs in Commutant Pairs ” S.H, & D. P. Jatkar. Mod.Phys.Lett.A 37 (2022) 29, 2250193 [arXiv:2101.12189 [hep-th]].
Details of my publications can be found on INSPIRE_HEP, Google Scholar or arXiv.
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