arXiv subjects

Arjun Bagchi

Publications and source records attributed to Arjun Bagchi.

At least 19 recordsLinked to original sources

arXiv2026

Scattering of Null strings - Flipped Vacuum & CHY

We investigate the scattering of null tensionless strings. Classical null strings, given by the ILST action, give rise to three distinct quantum theories built on different vacua and representations of the underlying 2d Conformal Carroll algebra (CCA) which form the residual gauge symmetries on the null worldsheet. In this paper, we are interested in the quantum theory built out of the so-called ``flipped'' vacuum which realises the highest weight representation of the 2d CCA. By considering a novel class of vertex operators, intimately connected to the compactified null string, we build scattering amplitudes of the theory. We show that one naturally obtains the Cachazo-He-Yuan (CHY) formulae when one considers scattering of massless states in the null ``flipped'' string.

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arXiv2026

Double Copy from the Flipped Null String

We study the double-copy structure of tree amplitudes of the bosonic null string in the flipped vacuum. We show that its level-one vector correlator supplies the Cachazo-He-Yuan (CHY) kinematic half-integrand of the higher-derivative $(DF)^2$ gauge theory, while distinguished compact momentum-winding sectors generate the complementary Parke-Taylor factor. For factorized level-two states, the same Carrollian world-sheet produces two kinematic half-integrands and hence the symmetric double copy to the six-derivative Weyl-cubed graviton sector. Lattice sectors with common external momenta reproduce the Bern-Carrasco-Johansson (BCJ) ordering relation and the corresponding field-theory Kawai-Lewellen-Tye (KLT) representation. These results provide a direct Carrollian world-sheet origin of the double copy and point toward a current-algebra realization of the emergent color sector compatible with the $O(d,d)$ structure of the compact lattice.

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arXiv2026

Doubly-scaled planar $\mathcal{N} = 4$ SYM & Carroll Holography

In their seminal paper, Okuda and Penedones (OP) put forward an intriguing proposal towards holography in asymptotically flat spacetimes (AFS). They showed that the flat space limit of 4 point bosonic tree-level string amplitude in AdS$_{5}\, \times\, S^{5}$ is dual to a specific double scaling limit of 4 point correlator in four dimensional (4d) $\mathcal{N} = 4$ super Yang-Mills (SYM) theory. In this paper, we show that the resulting boundary correlators can be used to define a 4d Carrollian conformal field theory (CFT) on future null infinity. This is done by mapping the set of doubly scaled correlators in SYM to null infinity, the conformal boundary of AFS. A Carroll CFT thus emerges in the infinite 't Hooft coupling limit of $\mathcal{N} = 4$ SYM. We extend the OP analysis to higher point functions and show how the Gram conditions on flat space amplitude put constraints on the double scaling limit of SYM correlators. We then use the soft factorization theorem for dilatonic string amplitude to write a recursion relation for the $({1}/{2})$-BPS sector of $\mathcal{N} = 4$ SYM in the double scaling limit. Finally, we show that the essential ideas underlying such a double scaling limit can be used as a tool-kit to build a class of Carrollian correlators, and hence define a Carrollian CFT, via certain integral transforms of flat space amplitudes of non-gravitational effective field theories.

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arXiv2026

Carrollian ABJM: Fermions and Supersymmetry

A natural approach for constructing a concrete example of flat space holography is to take the flat space limit of a well-understood example of AdS/CFT, such as the one relating M-theory in AdS$_4$ times an orbifolded 7-sphere to a certain three dimensional superconformal Chern-Simons-matter theory known as the ABJM theory living in the boundary of AdS$_4$. In particular, taking the flat space limit of the bulk corresponds to taking the speed of light $c$ to zero in the boundary, giving rise to a Carrollian superconformal theory. This limit is subtle to implement for fermions, however, since the Dirac algebra is sensitive to the spacetime metric and therefore takes a different form in Carrollian spacetimes than it does in Minkowski space. In fact, we show that there are four possible ways of realising Carrollian fermions, one of which arises at leading order in the $c\rightarrow0$ limit of relativistic fermions. In three dimensions, there is an additional complication that the minimal realisation of the Carrollian Dirac algebra requires $4\times4$ matrices rather than $2\times 2$ matrices familiar from the relativistic case. Nevertheless, we show that the $c\rightarrow0$ limit of the ABJM theory can be recast in terms of Carrollian Dirac matrices and enjoys and infinite-dimensional Carrollian superconformal symmetry whose bosonic subsector is the extended BMS$_4$ algebra encoding the asymptotic symmetries of four dimensional Minkowski space. This provides a concrete starting point for constructing a Carrollian gauge theory dual to M-theory in flat space.

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arXiv2026

Carroll fermions, expansions and the lightcone

We investigate fermions on Carrollian manifolds. We complement previous intrinsic analysis by deriving Carrollian fermion actions from a relativistic Dirac theory via a systematic expansion in the speed of light ($c$). We then study relativistic fermions in light-cone coordinates and their connection to Carrollian fermions in one lower dimension. This follows from the recent observation that the Poincar\'e algebra, written in lightcone coordinates contains (two) co-dimension one Carroll sub-algebras. Our results establish a clear bridge between intrinsic Carrollian constructions, small $c$-expansion and light-cone dynamics. In the process, we understand why Carrollian fermions in $D$-dimensions have features that relate them to relativistic fermions in both $D$ and $(D+1)$ dimensions.

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arXiv2026

High energy scattering and null strings

We propose an instrinsic worldsheet description of the ultra-high energy regime of string scattering based on worldsheet symmetries. At very high energies, the fundamental string becomes tensionless and in flat target spacetimes, the worldsheet becomes a null surface. Tensionless null strings thus emerge and the worldsheet symmetries morph from two copies of the Virasoro algebra to the two dimensional (2d) conformal Carroll or equivalently the 3d Bondi-van der Burgh-Metzner-Sachs (BMS) algebra. Tensionless strings have three inequivalent vacua over which they can be constructed, leading to distinct quantum theories. High energy tensile strings naturally connect to null strings built on the so-called induced vacuum. Our principle goal in this paper is the construction of scattering amplitudes for null strings in the induced vacuum. We show that these amplitudes, constructed from worldsheet methods of the null string, coincide with the high energy limit of usual string amplitudes. A crucial part of our analysis is the construction of integrated vertex operators. This achieved by relying on lessons from the parent string theory and following the tensionless limit carefully. A striking feature of the null string is the blurring of differences between open and closed strings. We see this at the level of the amplitudes as well. We then focus on four-point amplitudes and recover all expected regimes including the Gross-Mende regime and the Regge limit. We finally comment on a new class of vertex operators which arise naturally only in the zero tension string. This reproduces all our earlier analyses when put onshell but also has hints of signatures beyond the perturbative tensile string.

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arXiv2026

Black hole Near Horizons through the Looking Glass

We show that the near horizon of a generic non-extremal black hole (BH) can be understood in terms of a Carrollian geometry with two null directions, also called a String-Carroll (SC) geometry. The base space of this fibre-bundle structure is a sphere (or a plane for a black brane) and the fibre is the two-dimensional Rindler spacetime. We launch a detailed study of probes in this geometry. We study particle geodesics and scalar fields. The first part of the paper constructs geodesics and probe scalar fields directly in the SC geometry. We then look at a wide class of examples, including the Schwarzschild BH and the Kerr BH in asymptotically flat spacetimes, the BTZ BH and the black brane in AdS spacetimes, as well as Lifshitz black holes and construct the explicit maps to the SC geometry to obtain results specific to each case. These results are reproduced by considering the probe particles and fields in the original BH background and taking the near-horizon limit of the solutions. Our encyclopedia of examples establishes the notion of SC geometries as near-horizon geometries of non-extremal black objects, paving the way for a detailed, intricate future analysis of the quantum aspects of this geometry.

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arXiv2026

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.

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arXiv2025

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.

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arXiv2025

Universal sectors of two-dimensional Carrollian CFTs

We revisit modular invariance in two-dimensional Carrollian conformal field theories from a geometric perspective. Focusing on the characters of the induced and highest-weight representations of the theory, we show that there are regions of parameter space where the vacuum character dominates in the dual channel. We use this property to zoom into different subsectors of the Carrollian theory. One of them is reminiscent of the Schwarzian sector of a relativistic CFT2 and has a flat space holographic interpretation as O-plane orbifold. It exists only for the highest-weight representation. We prove that for all sectors with vacuum dominance in the dual channel, the specific heat is negative, concurrent with the holographic interpretation of the negative specific heat of asymptotically flat spacetimes with horizons.

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arXiv2025

The Carrollian Kaleidoscope

The Carroll group arises in the vanishing speed of light limit of the Poincar\'{e} group and was initially discarded as just a mathematical curiosity. However, recent developments have proved otherwise. Carroll and conformal Carroll symmetries are now ubiquitous, appearing in diverse physical phenomena starting from condensed matter physics to quantum gravity. This review aims to provide the reader a gateway into this fast-developing field. After an introduction and setting the stage with basics of the symmetry in question, we detail the construction of Carrollian and Carrollian Conformal field theories (CCFT). We then focus on applications. By far the most popular of these applications is in the context of the construction of holography in asymptotically flat spacetimes (AFS) in terms of a co-dimension one dual CCFT. We review the early work on AFS$_3$ /CCFT$_2$ before delving into an in-depth analysis for the construction of the dual to 4D AFS. Two other important sets of applications are in hydrodynamics and in condensed matter physics, which we discuss in detail. Carroll hydrodynamics is introduced as the $c\to 0$ limit of relativistic hydrodynamics first and then reconstructed from a symmetry based approach. Relations to ultrarelativistic flows and connections to the quark-gluon plasma are discussed with concrete examples of the Bjorken and Gubser flow models. In condensed matter applications, we cover connections to fractons, flat bands, and phase separation in Luttinger liquid models. To conclude, we give very brief outlines of other topics of interest including string theory and black hole horizons.

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arXiv2025

Scalar fields and 3D Flat Space Cosmologies

Flat Space Cosmologies (FSC) are time-dependent solutions in Einstein gravity in three-dimensional (3D) spacetimes with zero cosmological constant. These are orbifolds of 3D flat space that have a cosmological horizon and can be thought of as analogs of the Banados-Tietelboim-Zanelli (BTZ) black holes of AdS$_3$. We study scalar perturbations about these FSC solutions and explore the spectrum of quasi-normal modes (QNMs) crucially treating the cosmological horizon as a hard wall and extending to complex momenta. We connect this intrinsic analysis with the flatspace limit of the corresponding analysis in the BTZ black hole. The FSC QNMs are then utilized to build the scalar one-loop partition function by methods pioneered by Denef, Hartnoll and Sachdev in various simplifying limits and compared with existing answers in the literature.

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arXiv2025

Emergent Carroll symmetry at phase separation in one-dimensional lattice systems

Asymptotic behavior of generic Tomonaga-Luttinger liquid in the vicinity of phase-separated regions is known to produce an instability where well-known relativistic Conformal Field Theory (CFT) techniques fail. In this paper, we introduce an analytic paradigm that provides a continuum description of this important issue. We show that there is an emergent Carrollian symmetry when phase separation is reached, and techniques of Carroll CFT, as opposed to its relativistic relative, are central to the understanding of the physics. We work with the analogous spinless fermionic system in this region and capture the transition across this phase separation. Our numerical results corroborate the density-density correlations intrinsically computed using Carroll CFT. We further test the framework in a number of lattice systems, namely the spinless and spinfull fermionic models with distinct microscopic content, and find the same scaling at the transition. We discuss the scope of the framework and broader perspective.

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arXiv2024

Carroll in Shallow Water

We discover a surprising connection between Carrollian symmetries and hydrodynamics in the shallow water approximation. Carrollian symmetries arise in the speed of light going to zero limit of relativistic Poincar\'e symmetries. Using a recent gauge theoretic description of shallow water wave equations we find that the actions corresponding to two different waves, viz. the so called flat band solution and the Poincar\'e waves map exactly to the actions of the electric and magnetic sectors of Carrollian electrodynamics.

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arXiv2024

Strings, Virasoro Sandwiches and Worldsheet Horizons

We revisit the canonical quantization of free bosonic closed string theory and observe that the physicality of states requires vanishing of the worldsheet Virasoro algebra generators sandwiched between any two physical states. This requirement yields four classes of physical states, depending on discrete worldsheet symmetries: parity and time reversal. The usual string states which are highest weight states of the Virasoro algebra, preserve both, while the other new three classes break one or both. We apply our formulation to an accelerated worldsheet with horizons, initiating the worldsheet formulation of a thermal string theory and strings probing horizon of black holes.

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arXiv2024

Boundary Carrollian CFTs and Open Null Strings

We consider Carrollian conformal field theories in two dimensions and construct the boundary Carrollian conformal algebra (BCCA), opening up innumerable possibilities for further studies, given the growing relevance of Carrollian symmetries. We prove that the BCCA emerges by contracting a single copy of the Virasoro algebra. As an application, we construct, for the first time, open null strings and show that, for Dirichlet boundary conditions, we recover the BCCA as the algebra of constraints. We finally reconstruct our string results by taking the null limit of tensile open strings.

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arXiv2024

3D Stress Tensor for Gravity in 4D Flat Spacetime

Three dimensional (3d) Carrollian CFTs are potential co-dimension one holographic duals of 4d asymptotically flat spacetimes that live on the whole of the null boundary. In this paper, we show that the local stress tensor of the 3d Carrollian conformal theory (without any additional sources) constructed in terms of the geometric structure at asymptotic null infinity naturally encodes both the leading and subleading soft graviton theorems. We relate the 3d Carroll stress tensor to the 2d Celestial one and show how the 3d version naturally localises the non-local 2d Celestial stress tensor. We also comment on the relation with stress tensors in relativistic 3d CFTs and connections to the flat limit of AdS/CFT.

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arXiv2024

3d Carrollian Chern-Simons theory and 2d Yang-Mills

With the goal of building a concrete co-dimension one holographically dual field theory for four dimensional asymptotically flat spacetimes (4d AFS) as a limit of AdS$_4$/CFT$_3$, we begin an investigation of 3d Chern-Simons matter (CSM) theories in the Carroll regime. We perform a Carroll (speed of light $c\to0$) expansion of the relativistic Chern-Simons action coupled to a massless scalar and obtain Carrollian CSM theories, which we show are invariant under the infinite dimensional 3d conformal Carroll or 4d Bondi-van der Burg-Metzner-Sachs (BMS$_4$) symmetries, thus making them putative duals for 4d AFS. Concentrating on the leading-order electric Carroll CSM theory, we perform a null reduction of the 3d theory. Null reduction is a procedure to obtain non-relativistic theories from a higher dimensional relativistic theory. Curiously, null reduction of a Carrollian theory yields a relativistic lower-dimensional theory. We work with $SU(N) \times SU(M)$ CS theory coupled to bi-fundamental matter and show that when $N=M$, we obtain (rather surprisingly) a 2d Euclidean Yang-Mills theory after null reduction. We also comment on the reduction when $N \neq M$ and possible connections of the null-reduced Carroll theory to a candidate 2d Celestial CFT.

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