Dr. Arghya Chattopadhyay
department of physics, University of Puerto Rico-Mayaguez, Mayagüez, USA
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10Years (2017-Present)
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Representative Publications
View All Publications20 July 2023 in Physical Review D
Journal Article
Arghya ChattopadhyayAMArpita Mitra
Arpita MitraHZHendrik J. R. van Zyl
Hendrik J. R. van ZylWe demonstrate a relation between Nielsen’s approach toward circuit complexity and Krylov complexity through a particular construction of quantum state space geometry. We start by associating Kähler structures on the full projective Hilbert space of low rank algebras. This geometric structure of the states in the Hilbert space ensures that every unitary transformation of the associated algebras leave the metric and the symplectic forms invariant. We further associate a classical matter free Jackiw-Teitelboim gravity model with these state manifolds and show that the dilaton can be interpreted as the quantum mechanical expectation values of the symmetry generators. On the other hand, we identify the dilaton with the spread complexity over a Krylov basis thereby proposing a geometric perspective connecting two different notions of complexity.
7 August 2024 in Journal of High Energy Physics
Journal Article
We consider a perturbative expansion of the Lanczos coefficients and the Krylov complexity for two-dimensional conformal field theories under integrable deformations. Specifically, we explore the consequences of $$ \textrm{T}\overline{\textrm{T}} $$ , $$ \textrm{J}\overline{\textrm{T}} $$ , and $$ \textrm{J}\overline{\textrm{J}} $$ deformations, focusing on first-order corrections in the deformation parameter. Under $$ \textrm{T}\overline{\textrm{T}} $$ deformation, we demonstrate that the Lanczos coefficients b
n
exhibit unexpected behavior, deviating from linear growth within the valid perturbative regime. Notably, the Krylov exponent characterizing the rate of exponential growth of complexity surpasses that of the undeformed theory for positive value of deformation parameter, suggesting a potential violation of the conjectured operator growth bound within the realm of perturbative analysis. One may attribute this to the existence of logarithmic branch points along with higher order poles in the autocorrelation function compared to the undeformed case. In contrast to this, both $$ \textrm{J}\overline{\textrm{J}} $$ and $$ \textrm{J}\overline{\textrm{T}} $$ deformations induce no first order correction to either the linear growth of Lanczos coefficients at large-n or the Krylov exponent and hence the results for these two deformations align with those of the undeformed theory.
28 November 2017 in Journal of High Energy Physics
Journal Article
Arghya ChattopadhyayPDParikshit Dutta
Parikshit DuttaSDSuvankar Dutta
Suvankar DuttaWe show that large N phases of a 0 dimensional generic unitary matrix model (UMM) can be described in terms of topologies of two dimensional droplets on a plane spanned by eigenvalue and number of boxes in Young diagram. Information about different phases of UMM is encoded in the geometry of droplets. These droplets are similar to phase space distributions of a unitary matrix quantum mechanics (UMQM) ((0 + 1) dimensional) on constant time slices. We find that for a given UMM, it is possible to construct an effective UMQM such that its phase space distributions match with droplets of UMM on different time slices at large N . Therefore, large N phase transitions in UMM can be understood in terms of dynamics of an effective UMQM. From the geometry of droplets it is also possible to construct Young diagrams corresponding to U(N) representations and hence different large N states of the theory in momentum space. We explicitly consider two examples: single plaquette model with TrU 2 terms and Chern-Simons theory on S 3. We describe phases of CS theory in terms of eigenvalue distributions of unitary matrices and find dominant Young distributions for them.
17 May 2018 in Journal of High Energy Physics
Journal Article
Arghya ChattopadhyayPDParikshit Dutta
Parikshit DuttaSDSuvankar Dutta
Suvankar DuttaWe explicitly find representations for different large N phases of Chern-Simons matter theory on S2 × S1. These representations are characterised by Young diagrams. We show that no-gap and lower-gap phase of Chern-Simons-matter theory correspond to integrable representations of SU(N) k affine Lie algebra, where as upper-cap phase corresponds to integrable representations of SU(k − N) k affine Lie algebra. We use phase space description of [ 1 ] to obtain these representations and argue how putting a cap on eigenvalue distribution forces corresponding representations to be integrable. We also prove that the Young diagrams corresponding to lower-gap and upper-cap representations are related to each other by transposition under level-rank duality. Finally we draw phase space droplets for these phases and show how information about eigenvalue and Young diagram descriptions can be captured in topologies of these droplets in a unified way.
6 December 2019 in Physical Review D
Journal Article
Chern-Simons (CS) theories with rank and level on Seifert manifold are discussed. The partition functions of such theories can be written as a function of modular transformation matrices summed over different integrable representations of affine Lie algebra associated with the boundary Wess-Zumino-Witten model. Using properties of modular transform matrices we express the partition functions of these theories as a unitary matrix model. We show that the eigenvalues of unitary matrices are discrete and proportional to hook lengths of the corresponding integrable Young diagram. As a result, in the large limit, the eigenvalue density develops an upper cap. We consider CS theory on coupled with fundamental matters and express the partition functions in terms of modular transformation matrices. Solving this model at large we find the dominant integrable representations and show how large representations are related to each other by transposition of Young diagrams as a result of level rank duality. Next we consider CS theory on and observed that in Seifert framing the dominant representation is no longer an integrable representation after a critical value of ’t Hooft coupling. We also show that CS on admits multiple (two-gap phase) large phases with the same free energy.
1 May 2021 in Nuclear Physics B
Journal Article
Arghya ChattopadhyaySDSuvankar Dutta
Suvankar Dutta
DMDebangshu Mukherjee
Debangshu MukherjeeNENeetu
NeetuAbout Me
My research interests are quite varied. I get attracted to problems having challenging mathematical undertones, possibly allowing some algebraic geometry approach. This brought me closer to a lot of mathematical physics issues and specially string theory. At present I am working at the interface of theoretical physics and AI-driven experimental particle physics. By integrating machine-learning tools into both my formal studies (holography/mathematical physics) and hands-on work with Large hadron Collider open data, I am researching to bridge deep theory with real-time data applications.
Theoretical & Mathematical Physics: My research spans from 0D matrix models and 1D matrix quantum mechanics (mapping it to 2D Yang-Mills theory) through 2D Jackiw–Teitelboim gravity, CFTs and their integrable deformations, up to 3–4D higher-spin gravities and results in (non)-relativistic fluid/gravity duality for higher dimensions. At the 10D end, I study Calabi–Yau compactification, T-duality and Freudenthal duality in supergravity black holes, with side-projects in p-adic holography and other avenues of mathematical physics.
Experimental & AI-driven Applications: Alongside my theoretical endeavor, I’m developing machine-learning tools for jet physics and real-time data-quality monitoring for particle accelerators. My work on physics/symmetry-informed neural architectures further unites my theoretical insights with phenomenological and detector-level innovations.