Searcharxiv⌕ Search

arXiv subjects

Sarthak Duary

Publications and source records attributed to Sarthak Duary.

18 recordsLinked to original sources
arXiv2026

Tropical Open Strings in a Kalb-Ramond Background

We study tropical open strings arising from the analytically continued action of tropological sigma models in the presence of a constant Kalb-Ramond background. We show that the background field separates the theory into a generic sector and a critical sector. In the generic sector, the canonical structure produces a kinematical nonlocal bracket between the transverse and leafwise target-space coordinates. At the critical value of the Kalb-Ramond field, the Legendre map degenerates and the theory develops a primary constraint, requiring quantization by the Dirac-Bergmann procedure. This critical sector has a finite reduced phase-space structure and differs from the naive limit of the generic theory.

hep-th↗
arXiv2026

BRST quantization of Carroll-Weyl gauged null strings

We study the BRST quantization of the null string after completing its local gauge symmetry by Carroll-Weyl transformations. The resulting worldsheet theory possesses three first-class constraints, $C_1 = P^2$, $C_2 = P \cdot X'$, and $C_3 = P \cdot X$, whose modes realize a Weyl-BMS algebra. The additional Carroll-Weyl constraint qualitatively changes the quantum gauge complex: its scalar $s$-ghost is intrinsically coupled to the BMS $bc$-ghost sector, and the anomaly analysis involves three independent cocycles rather than a single Virasoro-type central charge. Starting from the gauge-fixed action, we derive the complete Faddeev-Popov complex, construct the matter and ghost currents and the BRST charge, and evaluate their equal-time operator products in the flipped, equivalently highest-weight, representation. The matter and ghost anomaly coefficients are $(c_{LL},c_{LS},c_{SS})_{\mathrm{matter}}=(2D,-D,-D)$ and $(c_{LL},c_{LS},c_{SS})_{\mathrm{ghost}}=(-54,6,4)$. Because the corresponding central terms multiply linearly independent ghost bilinears in $Q_B^2$, BRST nilpotency requires the three conditions $D=27$, $D=6$, and $D=4$, respectively. These conditions are mutually incompatible. Consequently, there is no target-space dimension in which the minimal flat Carroll-Weyl matter-plus-ghost complex is anomaly-free in the highest-weight representation. The familiar $D=26$ condition of the ILST null string is recovered only after truncation to the two-constraint BMS subsector, which defines a different quantum gauge complex.

hep-th↗
arXiv2026

Li\'enard--Wiechert fields in AdS and flat-space antipodal matching from geodesic-centered Coulombic data

We present a geometric derivation of Li\'enard--Wiechert fields in flat-space and AdS, emphasizing the origin of antipodal matching. In flat-space, the field of a uniformly moving charge is rewritten in coordinates centered on the source timelike geodesic. In this frame the charge is at rest and the solution is Coulombic, so the matching of the leading data at null infinity arises from describing a static field in a non-centered frame. We extend this construction to global AdS, where uniform motion is replaced by motion along a timelike geodesic. Starting from the static Coulomb solution at the center, we reconstruct the field of a freely moving charge in arbitrary global coordinates using embedding-space invariants. The resulting closed-form field obeys exact antipodal covariance in the bulk, and its boundary null-fringe limit reproduces the usual flat-space antipodal matching relation. We also describe an image-charge interpretation: the flat-space Coulomb field is represented after conformal compactification by an image singularity at spatial infinity, while the AdS Coulomb seed may be viewed as a charge together with an opposite image charge in a reflected copy. Together, these perspectives give a unified picture of Coulombic Li\'enard--Wiechert fields, antipodal matching, and the AdS-to-flat-space limit.

hep-th↗
arXiv2026

Path integral quantization of null bosonic strings with Carroll-Weyl ghosts

We revisit the path integral quantization of the null bosonic string from the viewpoint that all local gauge symmetries of the Carrollian worldsheet must be gauge fixed before the quantum theory is defined. In the tensile-string construction the $bc$ ghosts are the Faddeev-Popov determinant for fixing $\mathrm{Diff}\times\mathrm{Weyl}$. In the ILST null string this logic gives the BMS $bc$ system. However, a Carrollian worldsheet admits an additional volume-preserving Carroll-Weyl scaling, whose Hamiltonian generator is $C_3=P\cdot X$. Keeping this scaling as a genuine local gauge symmetry adds one more Faddeev-Popov row. The correct ghost system is therefore a $bcs$ system: the BMS $bc$ ghosts plus a scalar ghost $s$ and scalar antighost $b^s$ for Carroll-Weyl scaling. We derive the revised path integral, the $bcs$-ghost action, its residual symmetry equations, mode expansion, and its relation to the extended BMS algebra. The result changes the BRST complex and the anomaly problem: the usual $D=26$ check based only on the old BMS $bc$ ghosts is a partially gauge-fixed calculation, while the Carroll-Weyl covariant quantum theory must include the $s,b^s$ sector.

hep-th↗
arXiv2026

Finite-$N$ BMN index across all vacuum sectors

We compute the finite-$N$ Witten index of BMN matrix quantum mechanics after summing over all partition-labeled supersymmetric vacuum sectors. Starting from the unitary-matrix integral for each sector, we develop two complementary evaluation methods: a symmetric-group character expansion, which reduces each fixed fugacity order to a finite combinatorial sum, and a residue expansion in which the contributing poles are organized by rooted trees, with a colored-tree generalization for multi-partition sectors. Where practical, direct integration and extraction of the constant term in the expanded integrand give independent coefficient-by-coefficient checks. We evaluate every vacuum sector for $N\leq 9$. In the equal-fugacity expansion, the coefficients near charges $j\sim N^2$ show entropy growth of order $N^2$, and, in this range, the sector sum does not cancel this growth. The finite-$N$ data also reveal a nontrivial sectoral organization: near $j=N^2$, the sector giving the largest contribution changes with $N$, from single-partition sectors at small rank to double-partition sectors starting at $N=5$. We call this phenomenon dominance switching. These results provide quantitative finite-$N$ input for using the BMN index as a diagnostic of protected plane-wave black-hole sectors and suggest a D2 dressed black-hole interpretation in the controlled type-IIA regime, where D0 black-hole sectors are accompanied by macroscopic spherical D2-brane degrees of freedom, analogous to dual dressed black holes in $AdS_5\times S^5$.

hep-th↗
arXiv2026

Mass-Flow Invariance of $Q$-Cohomology in BMN Matrix Quantum Mechanics

We study the dependence of the dynamical supercharges of BMN matrix quantum mechanics on the mass parameter $μ$. Taking the $μ$-derivative at fixed canonical matrix variables, we show that the sixteen-component supercharge evolves by the adjoint action of a Hermitian quadratic bosonic operator $\mathcal{K}$, together with the spinor-space factor $iγ^{123}$. After projection to a $γ^{123}$-eigenspace, this flow integrates to a finite similarity transformation. For the nilpotent component $Q(μ)=\mathcal Q^4_-(μ)$, one obtains $Q(μ)=M(μ,μ_0)Q(μ_0)M(μ,μ_0)^{-1}$, giving an algebraic mass-flow non-renormalization statement for the $Q$-cohomology. The corresponding Hilbert-space statement has an analytic qualification, parallel to Witten's argument for supersymmetric quantum mechanics: $M$ is non-unitary and unbounded, so its action on the normalizable domain must be controlled. We formulate a small-step criterion by comparing the quadratic growth of $M$ with the Gaussian falloff of BMN oscillator wavefunctions within each component $μ>0$ or $μ<0$. As a concrete check, we evaluate this condition in the $N=2$ theory, whose two vacuum sectors are built on the trivial vacuum and the irreducible fuzzy-sphere vacuum. We also compute the induced $Q_{\rm BPS}$-action on the corresponding BPS letters: in the trivial sector it agrees with the standard BMN-sector BPS-letter differential of $\mathcal{N}=4$ SYM, while in the irreducible sector it vanishes.

hep-th↗
arXiv2026

From closed to open strings: the tensionless route in Kalb-Ramond background and noncommutativity

We study tensionless bosonic strings propagating in the presence of a constant Kalb--Ramond background and show how closed strings undergo a transition into open strings. Working in the intrinsically tensionless theory, we show that the Carrollian limit of the closed-string worldsheet induces a universal gluing of `left'- and `right'-moving oscillators, which is deformed in the presence of the background $B$-field. From the action we derive the mixed boundary conditions, construct the corresponding gluing matrix, and obtain the induced vacuum as a squeezed boundary state. This gives a first-principles realization of the closed-to-open string transition in the tensionless regime. We further extend the analysis to toroidal compactification and show that the worldsheet Bose--Einstein-like condensation mechanism continues to hold in the presence of the $B$-field. Second, we analyze boundary noncommutativity in a unified symplectic framework, both in the tensile theory and in the tensionless regime. In the tensile strings, we show that the boundary symplectic form reproduces the Seiberg--Witten noncommutative parameter. We then study the tensionless limit of this construction and show that the boundary $B$-field term remains as the unique surviving source of the symplectic structure. We derive the same structure directly in the intrinsically tensionless strings, where the inverse boundary symplectic form defines the noncommutative parameter of the null string.

hep-th↗
arXiv2026

Covariant phase space approach to noncommutativity in tensile and tensionless open strings

We study noncommutativity in open strings using the covariant phase space formalism. For tensile open strings in a constant Kalb-Ramond background, we show that the (pre)-symplectic current splits into a bulk kinetic term plus an exact boundary term, recovering the Seiberg-Witten noncommutativity parameter. We then extend the analysis to intrinsically tensionless strings. In the absence of background fields, the reduced phase space is degenerate and carries no intrinsic Poisson structure. In the presence of a constant Kalb-Ramond field, the symplectic current localises entirely on the boundary, so that the physical phase space becomes purely boundary-supported and the endpoint coordinates acquire a noncommutative Poisson algebra. Including a boundary gauge-field coupling similarly leads to a boundary symplectic form governed by the effective Born-Infeld combination on the D-brane. Our results provide a unified description of noncommutativity in both tensile and tensionless open strings.

hep-th↗
arXiv2025

Magnetic corrections to the classical soft photon theorems at all orders

When a set of charged or dyonic objects scatter and subsequently disperse, the process generically emits electromagnetic radiation. The classical soft photon theorem constrains the constant term and leading power-law fall-off of the emitted waveform at asymptotic times solely in terms of the momenta and charges of the incoming and outgoing particles. In this work, we extend the analysis to include the full tower of subleading corrections in the late-time and early-time expansion of the electric and magnetic waveforms, providing explicit expressions that depend only on the kinematic data and the electric and magnetic charges of the scattered objects. Using independent electric and magnetic potentials, we compute the full classical soft expansion for general dyonic scattering. We provide explicit, recursive expressions for the trajectory coefficients and the resulting electric and magnetic waveforms. The resulting soft expansion exhibits manifest covariance under the electric-magnetic duality. The electric and magnetic waveforms transform as an $SO(2)$ doublet under electric-magnetic duality. This provides a non-trivial consistency check on our formulation. For the specific case of two-body scattering, we obtain resummed expressions for the waveforms in both the time and frequency domains.

hep-th↗
arXiv2025

Waveform, memory and classical soft scalar theorems

We examine a scattering process in which a set of particles come together, interact through a long-range massless scalar force like dilaton mediated and then disperse. Using worldline formalism, we compute the trajectories of the scattered particles and derive an infinite series of subleading terms in the late-time and early-time expansion of the scalar waveform. We study the scalar waveform, the scalar memory term and classical soft scalar theorems. We ignore gravitational interactions and discuss the challenges if we include it.

hep-th↗
arXiv2025

Flat limit of AdS/CFT from AdS geodesics: scattering amplitudes and antipodal matching of Liénard-Wiechert fields

We revisit the flat limit of AdS/CFT from the point of view of geodesics in AdS. We show that the flat space scattering amplitudes can be constructed from operator insertions where the geodesics of the particles corresponding to the operators hit the conformal boundary of AdS. Further, we compute the Liénard-Wiechert solutions in AdS by boosting a static charge using AdS isometries and show that the solutions are antipodally matched between two regions, separated by a global time difference of $Δτ=π$. Going to the boundary of AdS along null geodesics, in the flat limit, this antipodal matching leads to the flat space antipodal matching near spatial infinity.

hep-th↗
arXiv2024

Flat limit of massless scalar scattering in $\mathrm{AdS}_2$

We explore the flat limit of massless scalar scattering in $\mathrm{AdS}_2$. We derive the $1 \to 1$ $\mathcal{S}$-matrix from the CFT $2$-point function. We show a key property of the $2 \to 2$ $\mathcal{S}$-matrix in $2d$, where the contact interaction in the flat limit gives momentum conserving delta function. We show the factorization of the $n \to n$ $\mathcal{S}$-matrix for integrable models in the flat limit, focusing on contact interactions. We calculate the $\mathcal{S}$-matrix by linking the CFT operator on the AdS boundary to the scattering state in flat-space. We use bulk operator reconstruction to study massless scalar scattering in the flat limit and solve the Klein-Gordon equation in global $\mathrm{AdS}_2$ for the massless scalar field. The solution is simple, involving a pure phase in global time and a sinusoidal function in the radial coordinate. This simplicity also extends to the smearing function, allowing us to map the scattering state to the CFT operator while taking AdS corrections into account.

hep-th↗
arXiv2024

Spectral representation in Klein space: simplifying celestial leaf amplitudes

In this paper, we explore the spectral representation in Klein space, which is the split $(2,2)$ signature flat spacetime. The Klein space can be foliated into Lorentzian $\mathrm{AdS}_3 /\mathbb{Z}$ slices, and its identity resolution has continuous and discrete parts. We calculate the identity resolution and the Plancherel measure in these slices. Using the foliation of Klein space into the slices, the identity resolution, and the Plancherel measure in each slice, we compute the spectral representation of the massive bulk-to-bulk propagator in Klein space. It can be expressed as the sum of the product of two massive (or tachyonic) conformal primary wavefunctions, with both continuous and discrete parts, and sharing a common boundary coordinate. An interesting point in Klein space is that, since the identity resolution has discrete and continuous parts, a new type of conformal primary wavefunction naturally arises for the massive (or tachyonic) case. For the conformal primary wavefunctions, both the discrete and continuous parts involve integrating over the common boundary coordinate and the real (or imaginary) mass. The conformal dimension is summed in the discrete part, whereas it is integrated in the continuous part. The spectral representation in Klein space is a computational tool to derive conformal block expansions for celestial amplitudes in Klein space and its building blocks, called celestial leaf amplitudes, by integrating the particle interaction vertex over a single slice of foliation.

hep-th↗
arXiv2022

AdS correction to the Faddeev-Kulish state: Migrating from the Flat Peninsula

The IR finiteness of $\mathcal{S}$-matrix in flat spacetime is tied to the Faddeev-Kulish dressed state, which suggests dressing the Fock space scattering state with the soft photon modes. We instigate a construction for the Faddeev-Kulish dressed state in the language of AdS/CFT. A salient feature of AdS spacetime is that it acquits itself as a quintessential IR regulator. The IR divergences will take shape after taking the zoomed in limit. We explore the Faddeev-Kulish dressed state to account for the AdS radius corrections. The Wilson line dressing stands as a guiding principle in the study of AdS radius-corrected Faddeev-Kulish dressing. We construct the modes of the Wilson line dressed massive scalar field implementing \textit{``vanilla HKLL reconstruction''} since the field is simply free field. This simplification is owing to the use of soft photon modes in the Wilson line dressing. We map the AdS radius-corrected soft photon modes in terms of CFT current operators. We invert this mapping, use the mapping in the Wilson line dressing, and express the AdS radius-corrected Faddeev-Kulish dressed state.

hep-th↗
arXiv2022

Celestial amplitude for 2d theory

We explore celestial amplitude corresponding to $2d$ bulk $\mathcal{S}$-matrix. We consider scalar particles with identical mass and show that the celestial amplitude becomes the fourier transform of the $2d$ $\mathcal{S}$-matrix written in the rapidity variable. We translate the crossing and unitarity conditions into the conditions on the celestial amplitude. For the $2d$ Sinh-Gordon model, we calculate the celestial amplitude perturbatively in coupling constant and check that the crossing and unitarity conditions are satisfied for the celestial amplitude. Imposing the crossing and unitarity conditions to the celestial amplitude, we want to find amplitudes to the higher order in perturbation theory from the lower order i.e., to provide a "\textit{proof of principle}" to show we can apply the bootstrap idea to the celestial amplitude. We find that imposing the crossing and unitarity conditions is not enough for bootstrapping celestial amplitude, there is an extra term which can't be fixed by the crossing and unitarity conditions. We also study the gravitational dressing condition in $2d$ QFT for massless particles in celestial space and see that for the gravitationally dressed celestial amplitude, the poles on the right half-plane get erased for several ansatzes.

hep-th↗
arXiv2022

Towards an IR finite S-matrix in the flat limit of AdS/CFT

Asymptotic Fock spaces lead to IR divergences in S-matrices. The issue can be traced back to the assumption of asymptotic decoupling, and its relaxation leads to Faddeev-Kulish states and an IR-finite S-matrix. In this paper we initiate the exploration of these states in the context of the flat limit of AdS/CFT. We construct asymptotic states as flat limits of fields that interact with the electro-magnetic field in AdS, and provide a reconstruction in terms of the dual CFT operators.

hep-th↗
arXiv2021

Adding Flavor to the Narain Ensemble

We revisit the proposal that the ensemble average over free boson CFTs in two dimensions - parameterized by Narain's moduli space - is dual to an exotic theory of gravity in three dimensions dubbed $U(1)$ gravity. We consider flavored partition functions, where the usual genus $g$ partition function is weighted by Wilson lines coupled to the conserved $U(1)$ currents of these theories. These flavored partition functions obey a heat equation which relates deformations of the Riemann surface moduli to those of the chemical potentials which measure these $U(1)$ charges. This allows us to derive a Siegel-Weil formula which computes the average of these flavored partition functions. The result takes the form of a "sum over geometries," albeit with modifications relative to the unflavored case.

hep-th↗