arXiv subjects

Mrigankamauli Chakraborty

Publications and source records attributed to Mrigankamauli Chakraborty.

5 recordsLinked to original sources

arXiv2026

Graphical Functions by Examples

Graphical functions have emerged as a powerful framework for evaluating multi-loop Feynman integrals in perturbative quantum field theory. Defined as massless three-point position-space integrals, they reveal rich analytic structures and have enabled major advances, including the highest-loop results currently known in several quantum field theories. Their role extends to conformal field theory, and recent algorithmic developments now allow many graphical functions to be computed automatically. This review, based on graduate-level lectures held by O.S. in 2025/26 at the University of Hamburg, introduces the central ideas behind graphical functions, covering periods, Feynman residues, and the treatment of regular and singular cases in both integer and non-integer dimensions. It also discusses connections to momentum space and self-duality, and provides guidance for further study, offering a coherent entry point into a topic not addressed in standard textbooks.

hep-th↗

arXiv2026

Connecting Supersymmetry to Non-Supersymmetric theories: the Gross-Neveu-Yukawa example

We construct a generalized Lagrangian that unifies the Gross-Neveu-Yukawa, Nambu-Jona-Lasinio-Yukawa, and Wess-Zumino models, allowing for arbitrary scalar and fermion flavors in $D$-dimensional regularization. This framework clarifies how emergent supersymmetry arises at critical points and reveals structural connections between these theories. The unified formulation provides additional supersymmetry Ward identities that simplify loop calculations, even for non-supersymmetric models. As an application, we show how this technique can reduce the computational cost of determining anomalous dimensions of twist-two operators.

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arXiv2026

Operator Renormalization using Emergent Supersymmetries

We develop a mechanism that enables supersymmetric Ward identities to be applied in non-supersymmetric theories. These identities are then used to streamline calculations in our target theories, potentially including phenomenological models. In these proceedings, we illustrate the method through operator renormalization in the Gross-Neveu-Yukawa model, where it leads to a significant optimization and a substantial reduction in computational effort. This serves as a toy example of the procedure that we ultimately aim to apply to Quantum Chromodynamics.

hep-th↗

arXiv2026

Dimensional Reduction is Supersymmetric at Three Loops

We resolve the long-standing claim that regularisation by dimensional reduction (DR) fails to preserve supersymmetry in Super Yang-Mills (SYM) theories at three loops. Earlier results reported a mismatch between the Yukawa and ghost-gluon $β$ functions in $\mathcal{N}=2$ SYM, suggesting a breakdown of supersymmertry. We show that this discrepancy does not originate from DR itself but from subtleties in the treatment of the Clifford algebra. A corrected three-loop calculation restores full supersymmetric behaviour, and we demonstrate that the same issue would first affect $\mathcal{N}=4$ SYM only at five loops, consistent with existing four-loop results. Our findings confirm that DR preserves supersymmetry for $\mathcal{N}=1, 2$ and $4$ SYM through the loop orders examined.

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arXiv2024

The asymptotic Hopf Algebra of Feynman Integrals

The method of regions is an approach for developing asymptotic expansions of Feynman Integrals. We focus on expansions in Euclidean signature, where the method of regions can also be formulated as an expansion by subgraph. We show that for such expansions valid around small/large masses and momenta the graph combinatorial operations can be formulated in terms of what we call the asymptotic Hopf algebra. This Hopf algebra is closely related to the motic Hopf algebra underlying the $R^*$ operation, an extension of Bogoliubov's $R$ operation, to subtract both IR and UV divergences of Feynman integrals in the Euclidean. We focus mostly on the leading power, for which the Hopf algebra formulation is simpler. We uncover a close connection between Bogoliubov's $R$ operation in the Connes-Kreimer formulation and the remainder $\mathcal{R}$ of the series expansion, whose Hopf algebraic structure is identically formalised in the corresponding group of characters. While in the Connes-Kreimer formulation the UV counterterm is formalised in terms of a twisted antipode, we show that in the expansion by subgraph a similar role is played by the integrand Taylor operator. To discuss the structure of higher power expansions we introduce a novel Hopf monoid formulation.

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