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Ritankar Chatterjee

Publications and source records attributed to Ritankar Chatterjee.

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Towards a Holographic dual of Carrollian BCFT

In this work we aim to lay the foundation of flat version of AdS$_3$/BCFT$_2$ correspondence through Carrollian framework. We begin with discussing the recently discovered Boundary Carrollian Conformal Algebra (BCCA), the symmetry algebra of Carrollian BCFT. We identify this algebra at the null infinity of flat spacetime with appropriate choice of the end-of-the-world (EOW) brane. The properties of this EOW brane have been analysed both intrinsically and by taking flat limit from its AdS counterpart. We also find that the global as well as asymptotic symmetries of flat spacetime restricted by this EOW brane coincide exactly with the symmetries of BCCA.

hep-th

The Tensionless Lives of Null Strings

The tensionless limit probes the very high energy regime of string theory in contrast to the well studied point-particle limit which reduces to Einstein gravity. Tensionless strings sweep out null worldsheets in the target space and hence are also called null strings. This article aims to provide a comprehensive review of tensionless null string theory beginning with the initial work of Schild, and continuing to the foundational work of Isberg et al (ILST) and then focussing on developments in the past decade. Recent work centres on the emergence of the Carrollian Conformal Algebra as residual worldsheet symmetries of the ILST action and the identification of tensionless limit as a worldsheet Carrollian limit on the string worldsheet. Carrollian structures are used to address the classical and quantum aspects of the null string. In the classical theory, the aforementioned limit agrees with the analysis from the ILST action. Symmetries, constraints, mode expansions computed from both perspectives match nicely providing a robust cross-check of the analyses. We discuss closed and open null strings as well as their supersymmetric cousins. The quantum null string comes with several surprises, the foremost of which is the emergence of three consistent quantum theories from the ILST action. We detail the canonical quantisation and the spectrum of the triumvirate of theories. We discuss the novelties of the quantum null theories and the effect compactifaction has on them. We also discuss Carroll strings, applications of these ideas to strings approaching black holes and give a quick overview of other related developments.

hep-th

Boundary Carroll CFTs: SUSY and Superstrings

We consider two dimensional superconformal Carrollian theories with boundaries and construct two variants of the Boundary Superconformal Carrollian Algebra (BSCCA), viz. the Homogeneous and the Inhomogeneous, by making appropriate identification of the parent superconformal Carrollian algebras. These new algebras are then recovered by appropriate limits of a single copy of Super Virasoro algebra. We then focus on the theory of null tensionless superstrings and construct, for the first time, an open null superstring. The Homogeneous version of the BSCCA is realised as worldsheet symmetries on this open null superstring.

hep-th

Tensionless Strings in a Kalb-Ramond Background

We investigate tensionless (or null) bosonic string theory with a Kalb-Ramond background turned on. In analogy with the tensile case, we find that the Kalb-Ramond field has a non-trivial effect on the spectrum only when the theory is compactified on an (\left(S^1\right)^{\otimes d}) background with (d\geq 2). We discuss the effect of this background field on the tensionless spectrum constructed on three known consistent null string vacua. We elucidate further on the intriguing fate of duality symmetries in these classes of string theories when the background field is turned on.

hep-th

Tensionless Tales of Compactification

We study circle compactifications of tensionless bosonic string theory, both at the classical and the quantum level. The physical state condition for different representations of BMS$_3$, the worldsheet residual gauge symmetry for tensionless strings, admits three inequivalent quantum vacua. We obtain the compactified mass spectrum in each of these vacua using canonical quantization and explicate their properties.

hep-th

Non-Lorentzian Ka\v{c}-Moody Algebras

We investigate two dimensional (2d) quantum field theories which exhibit Non- Lorentzian Ka\v{c}-Moody (NLKM) algebras as their underlying symmetry. Our investigations encompass both 2d Galilean (speed of light $c \rightarrow \infty$) and Carrollian ($c \rightarrow 0$) CFTs with additional number of infinite non-Abelian currents, stemming from an isomorphism between the two algebras. We alternate between an intrinsic and a limiting analysis. Our NLKM algebra is constructed first through a contraction and then derived from an intrinsically Carrollian perspective. We then go on to use the symmetries to derive a Non-Lorentzian (NL) Sugawara construction and ultimately write down the NL equivalent of the Knizhnik Zamolodchikov equations. All of these are also derived from contractions, thus providing a robust cross-check of our analyses.

hep-th

BMS Field Theories with $\mathfrak{u}(1)$ Symmetry

We investigate quantum field theories in two dimensions (2d) with an underlying Bondi-van der Burgh-Metzner-Sachs (BMS) symmetry augmented by $\mathfrak{u}(1)$ currents. These field theories are expected to holographically capture features of charged versions of cosmological solutions in asymptotically flat 3d spacetimes called Flat Space Cosmologies (FSCs). We conduct a study of the modular properties of these field theories. The characters for the highest weight representations of the symmetry algebra are constructed, and the partition function of the theory is obtained from them. We derive the density of (primary) states and find the entropy and asymptotic values of the structure constants exploiting the modular properties of the partition function and the torus one-point function. The expression for the asymptotic structure constants shows shifts in the weights and one of the central terms and an extra phase compared to the earlier results in the literature for BMS invariant theories without $\mathfrak{u}(1)$ currents present. We reproduce our field results for the structure constants by a bulk computation involving a scalar probe in the background of a charged FSC.

hep-th

A Rindler Road to Carrollian Worldsheets

The tensionless limit of string theory has recently been formulated in terms of worldsheet Rindler physics. In this paper, by considering closed strings moving in background Rindler spacetimes, we provide a concrete exemplification of this phenomenon. We first show that strings probing the near-horizon region of a generic non-extremal blackhole become tensionless thereby linking a spacetime Carroll limit to a worldsheet Carroll limit. Then, considering strings in $d$-dimensional Rindler spacetime we find a Rindler structure induced on the worldsheet. Novelties, including folds, appear on the closed string worldsheet pertaining to the formation of the worldsheet horizon. The closed string becomes segmented at these folding points and different segments go into the formation of closed strings in the different Rindler wedges. The Bondi-Metzner-Sachs (BMS) or the Conformal Carroll algebra emerges from the closed string Virasoro algebra as the horizon is hit. Quantum states on these accelerated worldsheets are discussed and we show the formation of boundary states from gluing conditions of the different segments of the accelerated closed string.

hep-th