Browsing by Author "Banerjee, Aritra"

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Beyond Wilson? Carroll from current deformations
(Springer, 2024) Banerjee, Aritra
At extreme energies, both low and high, the spacetime symmetries of relativistic quantum field theories (QFTs) are expected to change with Galilean symmetries emerging in the very low energy domain and, as we will argue, Carrollian symmetries appearing at very high energies. The formulation of Wilsonian renormalisation group seems inadequate for handling these changes of the underlying Poincare symmetry of QFTs and it seems unlikely that these drastic changes can be seen within the realms of relativistic QFT. We show that contrary to this expectation, changes in the spacetime algebra occurs at the very edges of parameter space. In particular, we focus on the very high energy sector and show how bilinears of U(1) currents added to a two dimensional (massless) scalar field theory deform the relativistic spacetime conformal algebra to conformal Carroll as the effective coupling of the deformation is dialed to infinity. We demonstrate this using both a symmetric and an antisymmetric current-current deformation for theories with multiple scalar fields. These two operators generate distinct kinds of quantum flows in the coupling space, the symmetric driven by Bogoliubov transformations and the antisymmetric by spectral flows, both leading to Carrollian CFTs at the end of the flow.
Boosting to BMS
(Springer, 2022-09) Banerjee, Aritra
Bondi-Metzner-Sachs (BMS) symmetries, or equivalently Conformal Carroll symmetries, are intrinsically associated to null manifolds and in two dimensions can be obtained as an Inönü-Wigner contraction of the two-dimensional (2d) relativistic conformal algebra. Instead of performing contractions, we demonstrate in this paper how this transmutation of symmetries can be achieved by infinite boosts or degenerate linear transformations on coordinates. Taking explicit cues from the worldsheet theory of null strings, we show boosting the system is equivalent to adding a current-current deformation term to the Hamiltonian. As the strength of this deformation term reaches a critical value, the classical symmetry algebra “flows” from two copies of Virasoro to the BMS algebra. We further explore the situation where the CFT coordinates are asymmetrically transformed, and degenerate limits lead to chiral theories.
Bootstrapping the Kronig-Penney Model
(APS, 2022-12) Banerjee, Aritra
Recently, bootstrap methods from conformal field theory have been adapted for studying the energy spectrum of various quantum mechanical systems. In this paper, we consider the application of these methods in obtaining the spectrum from the Schrödinger equation with periodic potentials, paying particular attention to the Kronig-Penney model of a particle in a one-dimensional lattice. With an appropriate choice of operator basis involving position and momenta, we find that the bootstrap approach efficiently computes the band gaps of the energy spectrum but has trouble effectively constraining the minimum energy. We show how applying more complex constraints involving higher powers of momenta can potentially remedy such a problem. We also propose an approach for analytically constructing the dispersion relation associated with the Bloch momentum of the system.
Carroll covariant scalar fields in two dimensions
(Springer, 2023-01) Banerjee, Aritra
Conformal Carroll symmetry generically arises on null manifolds and is important for holography of asymptotically flat spacetimes, generic black hole horizons and tensionless strings. In this paper, we focus on two dimensional (2d) null manifolds and hence on the 2d Conformal Carroll or equivalently the 3d Bondi-Metzner-Sachs (BMS) algebra. Using Carroll covariance, we write the most general free massless Carroll scalar field theory and discover three inequivalent actions. Of these, two viz. the time-like and space-like actions, have made their appearance in literature before. We uncover a third that we call the mixed-derivative theory. As expected, all three theories enjoy off-shell BMS invariance. Interestingly, we find that the on-shell symmetry of mixed derivative theory is a single Virasoro algebra instead of the full BMS. We discuss potential applications to tensionless strings and flat holography.
Carroll fermions in two dimensions
(APS, 2023-06) Banerjee, Aritra
Carroll symmetry is a very powerful characteristic of generic null surfaces, as it replaces the usual Poincaré algebra with a vanishing speed of light version thereof. These symmetries have found universal applications in the physics of null manifolds as they arise in diverse situations ranging from black hole horizons to condensed matter systems with vanishing Fermi velocities. In this work, we concentrate on fermions living on two-dimensional (2⁢𝑑) null manifolds and explore the Carroll invariant structure of the associated field theories in a systematic manner. The free massless versions of these fermions are shown to exhibit 2⁢𝑑 conformal Carroll or, equivalently the 3⁢𝑑 Bondi-Metzner-Sachs (BMS) algebra as their symmetry. Due to the degenerate nature of the manifold, we show the presence of two distinct classes of Clifford algebras. We also find that in two dimensions, there are two distinct fermion actions. We study discrete and continuous symmetries of both theories and quantise them using the highest weight representation of the vacuum. We also discuss how the symmetries of 2⁢𝑑 free fermion conformal field theories can be continually deformed by infinite boosts or degenerate linear transformations on coordinates, leading to the corresponding BMS invariant theory at singular points.
Cosmography and flat Λ⁢CDM tensions at high redshift
(APS, 2020-12) Banerjee, Aritra
Risaliti, Lusso, and collaborators have constructed a high-redshift Hubble diagram of supernovae (SNe), quasars (QSO), and gamma-ray bursts (GRBs) that shows a “∼4⁢𝜎 tension with the Λ⁢CDM model” based on a log polynomial cosmographic expansion [1,2]. In this work, we demonstrate that the log polynomial expansion generically fails to recover flat Λ⁢CDM beyond 𝑧∼2, thus undermining the ∼4⁢𝜎 tension claim. Moreover, through direct fits of both the flat Λ⁢CDM and the log polynomial model to the SNe+QSO+GRB data set, we confirm that the flat Λ⁢CDM model is preferred. Ultimately, we trace the tension to the QSO data and show that a best fit of the flat Λ⁢CDM model to the QSO data leads to a flat Λ⁢CDM universe with no dark energy within 1⁢𝜎. This marks an irreconcilable tension between the Risaliti-Lusso QSOs and flat Λ⁢CDM.
D1 string dynamics in curved backgrounds with fluxes
(Springer, 2016) Banerjee, Aritra
We study various rotating and oscillating D-string configurations in some general backgrounds with fluxes. In particular, we look for solutions to the equations of motion of various rigidly rotating D-strings in AdS3 background with mixed flux, and in the intersecting D-brane geometries. We find out relations among various conserved charges corresponding to the breathing and rotating D-string configurations.
Ehlers transformations as EM duality in the double copy
(APS, 2020-12) Banerjee, Aritra
Given a solution to 4D Einstein gravity with an isometry direction, it is known that the equations of motion are identical to those of a 3D 𝜎 model with target space geometry 𝑆⁢𝑈⁡(1,1)/𝑈⁡(1). Thus, any transformation by 𝑆⁢𝑈⁡(1,1)≅𝑆⁢𝐿⁡(2,ℝ) is a symmetry for the action and allows one to generate new solutions in 4D. Here we clarify and extend recent work on electromagnetic (EM) duality in the context of the classical double copy. In particular, for pure gravity, we identify an explicit map between the Maxwell field of the single copy and the scalars in the target space, allowing us to identify the 𝑈⁡(1)⊂𝑆⁢𝐿⁡(2,ℝ) symmetry dual to EM duality in the single copy. Moreover, we extend the analysis to Einstein-Maxwell theory, where we highlight the role of Ehlers-Harrison transformations and, for spherically symmetric charged black hole solutions, we interpret the equations of motion as a truncation of the putative single copy for Einstein-Yang-Mills theory.
Entanglement entropy for TT deformed CFT in general dimensions
(Elsevier, 2019-11) Banerjee, Aritra
We consider deformation of a generic d dimensional () large-N CFT on a sphere by a spin-0 operator which is bilinear in the components of the stress tensor. Such a deformation has been proposed to be holographically dual to an bulk with a hard radial cut-off. We compute the exact partition function and find the entanglement entropy from the field theory side in various dimensions and compare with the corresponding holographic results. We also compute renormalized entanglement entropy both in field theory and holography and find complete agreement between them.
Exotic origins of tensionless superstrings
(Elsevier, 2020-02) Banerjee, Aritra
A new type of tensionless superstring theory, called the Inhomogeneous tensionless superstring, has been recently introduced. This is characterised by a residual symmetry algebra on the worldsheet richer in structure than the previously known symmetry algebra related to Homogeneous tensionless superstring. In this paper, we investigate theories of tensile superstring that the Inhomogeneous tensionless superstring with manifestly real fermions could arise from. We provide two different candidates for these parent tensile theories. The nature of the limit dictates that these theories have some exotic features.
Fast spinning strings on η deformed AdS5 × S5
(Springer, 2018-02) Banerjee, Aritra
In this paper, considering the correspondence between spin chains and string sigma models, we explore the rotating string solutions over η deformed AdS5 × S5 in the so-called fast spinning limit. In our analysis, we focus only on the bosonic part of the full superstring action and compute the relevant limits on both (R × S3) η and (R × S5) η models. The resulting system reveals that in the fast spinning limit, the sigma model on η deformed S5 could be approximately thought of as the continuum limit of anisotropic SU(3) Heisenberg spin chain model. We compute the energy for a certain class of spinning strings in deformed S5 and we show that this energy can be mapped to that of a similar spinning string in the purely imaginary β deformed background.
Flat bands and compact localised states: a carrollian roadmap
(SciPost Foundation, 2025-08) Banerjee, Aritra
We show how Carrollian symmetries become important in the construction of one-dimensional fermionic systems with all flat-band spectra from first principles. The key ingredient of this construction is the identification of Compact Localised States (CLSs), which appear naturally by demanding supertranslation invariance of the system. We use CLS basis states, with inherent ultra-local correlations, to write down an interacting theory which shows a non-trivial phase structure and an emergent Carroll conformal symmetry at the gapless points. We analyze this theory in detail for both zero and finite chemical potential.
From CFTs to theories with Bondi-Metzner-Sachs symmetries: Complexity and out-of-time-ordered correlators
(2022-03) Banerjee, Aritra
We probe the contraction from 2d relativistic CFTs to theories with Bondi-Metzner-Sachs (BMS) symmetries, or equivalently Conformal Carroll symmetries, using diagnostics of quantum chaos. Starting from an Ultrarelativistic limit on a relativistic scalar field theory and following through at the quantum level using an oscillator representation of states, one can show the CFT2 vacuum evolves smoothly into a BMS3 vacuum in the form of a squeezed state. Computing circuit complexity of this transmutation using the covariance matrix approach shows clear divergences when the BMS point is hit or equivalently when the target state becomes a boundary state. We also find similar behaviour of the circuit complexity calculated from methods of information geometry. Furthermore, we discuss the hamiltonian evolution of the system and investigate Out-of-time-ordered correlators (OTOCs) and operator growth complexity, both of which turn out to scale polynomially with time at the BMS point.
Hubble sinks in the low-redshift swampland
(APS, 2021) Banerjee, Aritra
Local determinations of the Hubble constant 𝐻0 favor a higher value than Planck based on cosmic microwave background and Λ cold dark matter (Λ⁢CDM). Through a model-independent expansion, we show that low redshift (𝑧≲0.7) data comprising baryon acoustic oscillations, cosmic chronometers, and Type Ia supernovae have a preference for quintessence models that lower 𝐻0 relative to Λ⁢CDM. In addition, we confirm that an exponential coupling to dark matter cannot alter this conclusion in the same redshift range. Our results leave open the possibility that a coupling in the matter-dominated epoch, potentially even in the dark ages, may yet save 𝐻0 from sinking in the string theory swampland.
Inhomogeneous Tensionless Superstrings
(Springer, 2018-02) Banerjee, Aritra
We construct a novel tensionless limit of Superstring theory that realises the Inhomogeneous Super Galilean Conformal Algebra (SGCA I ) as the residual symmetry in the analogue of the conformal gauge, as opposed to previous constructions of the tensionless superstring, where a smaller symmetry algebra called the Homogeneous SGCA emerged as the residual gauge symmetry on the worldsheet. We obtain various features of the new tensionless theory intrinsically as well as from a systematic limit of the corresponding features of the tensile theory. We discuss why it is desirable and also natural to work with this new tensionless limit and the larger algebra.
Magic Fermions: Carroll and Flat Bands
(Springer, 2023-03) Banerjee, Aritra
The Carroll algebra is constructed as the c → 0 limit of the Poincare algebra and is associated to symmetries on generic null surfaces. In this paper, we begin investigations of Carrollian fermions or fermions defined on generic null surfaces. Due to the availability of two different (degenerate) metrics on Carroll spacetimes, there is the possibility of two different versions of Carroll Clifford algebras. We consider both possibilities and construct explicit representations of Carrollian gamma matrices and show how to build higher spacetime dimensional representations out of lower ones. Actions for Carroll fermions are constructed with these gamma matrices and the properties of these actions are investigated. We show that in condensed matter systems where the dispersion relation becomes trivial i.e. the energy is not dependent on momentum and bands flatten out, Carroll symmetry generically appears. We give explicit examples of this including that of twisted bi-layer graphene, where superconductivity appears at so called magic angles and connect this to Carroll fermions.
ModMax meets GCA
(2022-06) Banerjee, Aritra
A maximally symmetric non-linear extension of Maxwell's theory in four dimensions called ModMax has been recently introduced in the literature. This theory preserves both electromagnetic duality and conformal invariance of the linear theory. In this short paper, we introduce a Galilean cousin of the ModMax theory, written in a covariant formalism, that is explicitly shown to be invariant under Galilean Conformal Symmetries. We discuss the construction of such a theory involving Galilean electromagnetic invariants, and show how the classical structure of the theory is invariant under the action of Galilean Conformal Algebra (GCA).
Multi-spike strings in AdS3 with mixed three-form fluxes
(Springer, 2016-05) Banerjee, Aritra
The string sigma model in AdS3 ×S 3 supported by mixed three-form fluxes has recently been proved to be integrable which led to a plethora of work in this background including proposals for S matrix and study of semiclassical string profiles. Motivated by this, in this paper, we present a study of ‘spiky’ strings in this background. We analyze the string profiles in detail and also find the dispersion relation between the charges in the ‘long’ string limit after solving the equations of motion perturbatively upto the leading order in the Neveu-Schwarz flux b. We find that the dispersion for 2 spikes gets corrected by the term log S. We also discuss the fate of the solution in the limit of pure NS-NS flux.
A note on oscillating strings in AdS3×S3 with mixed three-form fluxes
(Springer, 2015) Banerjee, Aritra
We present a detailed study of the pulsating string solutions in AdS3 × S 3 supported by both RR and NS-NS fluxes. This background has recently been proved to be integrable. We find the dispersion relation between the energy, oscillation number and other conserved charges when the NS-NS flux turned on is small. We further discuss the fate of the string solutions in pure RR and NS-NS cases.
On circular strings in (AdS3 ×S3)_k , Aritra Banerje
(Springer, 2016) Banerjee, Aritra
The so called one-parameter (often called ϰ) deformed AdS string sigma models have attracted a lot of attention lately in the study of integrability in string theory. We construct various circular string solutions in the (AdS3 × S 3) ϰ background and describe the characteristics of such solutions qualitatively. We study the Bohr-Sommerfeld like quantization for these string states to characterise the motion. Further we find a ‘long’ string limit of such circular strings in the ϰ-deformed AdS3 and find a novel dependence of the oscillation number on the energy in the next to leading order expansion.