arXiv subjects

Kamal L. Panigrahi

Publications and source records attributed to Kamal L. Panigrahi.

At least 19 recordsLinked to original sources

arXiv2026

Holographic Extended Thermodynamics of deformed AdS-Schwarzschild black hole

We investigate the thermodynamics and phase structure of the deformed AdS-Schwarzschild black hole, generated via the gravitational decoupling (GD) method. In the bulk canonical ensemble, our results exhibit a van der Waals-type first-order phase transition in addition to the Hawking-Page transition, in the suitable parameter regime. Further, we compute the critical exponents characterising the bulk transition, confirming their consistency with mean-field theory predictions. Exploiting the exact holographic dictionary between extended black hole thermodynamics and the dual conformal field theory (CFT), we extend this analysis to the boundary and uncover a rich array of phase transitions and critical phenomena across three distinct thermodynamic ensembles. In particular, in the fixed $(\mathcal{V},C)$ ensemble, the dual CFT exhibits a Hawking-Page-type transition. However, in the fixed $(p,C)$ ensemble, the deformation parameter leads to a distinct thermodynamic behaviour in which multiple branches become unstable, leaving a single thermodynamically stable phase, thus marking a clear departure from the standard van der Waals scenario. Throughout, we emphasise the pivotal influence of the GD deformation parameter on the thermodynamic behaviour, and we elucidate its role in the confinement-deconfinement transitions characteristic of the deformed AdS-Schwarzschild geometry.

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arXiv2025

Investigating (Non)-Integrability and Pulsating String in D3-Brane Background

This work explores the (non)-integrability and chaotic dynamics of classical strings in the background of a D3-brane with a non-commutative parameter, within the framework of the AdS/CFT correspondence. Using the Polyakov action, we derive the equations of motion and constraints for pulsating strings and analyze their stability through perturbation theory. In the high-energy limit, the first-order perturbed equation simplifies to the Pöschl-Teller equation, solvable via associated Legendre or hypergeometric functions, while numerical methods are employed for generic energy values. We demonstrate that the non-commutative parameter enhances chaotic behavior, as evidenced by the Largest Lyapunov Exponent (LLE). Furthermore, we investigate the integrability of geodesic motion and identify two distinct string modes: captured at and escape to infinity. Finally, we study pulsating strings in the deformed $(AdS_{3} \times S^{2})_{\varkappa}$ background, deriving dispersion relations for both short and long strings.

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arXiv2025

Chaos Bound and its violation in Black p-brane

In this work, we have extensively investigated the dynamics of circular geodesic (chargeless massive particle) followed by the investigation of the pulsating classical string in the p-brane background. This study is a continuation of our previous work JHEP10(2023)189, in which we numerically identified the presence of chaos for a classical string hovering near generic p-branes ($p < 7$). Here, for a particle probe, we have found evidence of chaos in the vicinity of the horizon. Furthermore, we observed a violation of the well-known MSS bound in specific extremal p-branes; however, no such violation is seen in the non-extremal cases. Similar observations were made for the classical string, where the violation of the bound is significant near the horizon. Thus, our semi-analytical arguments demonstrate that chaotic dynamics in black p-branes exhibit the (generalized) universal bound with notable violations, regardless of whether a particle or classical string is used as a probe.

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arXiv2024

Lyapunov spectra and fluctuation relations: Insights from the Galerkin-truncated Burgers equation

The imposition of a global constraint of the conservation of total kinetic energy on a forced-dissipative Burgers equation yields a governing equation that is invariant under the time-reversal symmetry operation, $\{\mathcal{T}: t \to -t; u \to -u \}$, where $u$ is the velocity field. Moreover, the dissipation term gets strongly modified, as the viscosity is no longer a constant, but a fluctuating, state dependent quantity, which can even become negative in certain dynamical regimes. Despite these differences, the statistical properties of different dynamical regimes of the time-reversible Burgers equation and the standard forced-dssipative Burgers equation are equivalent, à la Gallavotti's conjecture of \textit{equivalence of nonequilibrium ensembles}. We show that the negative viscosity events occur only in the thermalized regime described by the time-reversible equation. This quasi-equilibrium regime is examined by calculating the local Lyapunov spectra and fluctuation relations. A pairing symmetry among the spectra is observed, indicating that the dynamics is chaotic and has an attractor spanning the entire phase space of the system. The violations of the second law of thermodynamics are found to be in accordance with the fluctuation relations, namely the Gallavotti-Cohen relation based on the phase-space contraction rate and the Cohen-Searles fluctuation relation based on the energy production rate. It is also argued that these violations are associated with the effects of the Galerkin-truncation, the latter is responsible for the thermalization.

nlin.CD↗

arXiv2023

Circular string in a Black p-brane leading to chaos

We consider a pulsating string near a non-extremal black p-brane (p=5 and p=6) and investigate the chaos in the corresponding string dynamics by examining the Fast Lyapunov indicator(FLI) and Poincare section. In our system, the energy and the charge play the role of control parameters. For generic values of these parameters, the numerical results show that the dynamics primarily fall into three modes: capture, escape to infinity, and quasiperiodic depending on the initial location (near to or far away from the black brane horizon) of the string. Finally, probing for different values of the winding number (n) the dynamics turns out to be sensitive to n. In particular, we observe the point particle (n=0) scenario to be integrable whereas at higher n the dynamics seems to be chaotic.

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arXiv2022

Neumann-Rosochatius system for strings on I-brane

We study rigidly rotating and pulsating strings in the background of a 1+1 dimensional intersection of two orthogonal stacks of fivebranes in type IIB string theory by using the Neumann-Rosochatius (NR) model. Starting with the Polyakov action of the probe fundamental string we show that a generalised ansatz reduce the system into the one dimensional NR model in the presence of flux. The integrable construction of the model is exploited to analyze the rotating and oscillating string solution. We render the large $J$ BMN-type expansion for the energy of rotating string states while the same for the oscillating string has been derived in long string and small angular momenta limit.

hep-th↗

arXiv2022

Neumann-Rosochatius system for rotating strings in $AdS_3 \times S^3\times S^3\times S^1$ with flux

Strings on $AdS_3 \times S^3\times S^3\times S^1$ with mixed flux exhibit exact integrability. We wish to construct an integrable Neumann-Rosochatius (NR) model of strings starting with the type IIB supergravity action in $AdS_3 \times S^3\times S^3\times S^1$ with pure NSNS flux. We observe that the forms of the Lagrangian and the Uhlenbeck integrals of motion of the considered system are NR-like with some suitable deformations which eventually appear due to the presence of flux. We utilize the integrable framework of the deformed NR model to analyze rigidly rotating spiky strings moving only in $S^3\times S^1$. We further present some mathematical speculations on the rounding-off nature of the spike in the presence of non-zero angular momentum $J$ in $S^1$.

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arXiv2021

$N$-spike string in $AdS_3 \times S^1$ with mixed flux

Sigma model in $AdS_3\times S^3$ background supported by both NS-NS and R-R fluxes is one of the most distinguished integrable models. We study a class of classical string solutions for $N$-spike strings moving in $AdS_3 \times S^1$ with angular momentum $J$ in $S^1 \subset S^5$ in the presence of mixed flux. We observe that the addition of angular momentum $J$ or winding number $m$ results in the spikes getting rounded off and not end in cusp. The presence of flux shows no alteration to the rounding-off nature of the spikes. We also consider the large $N$-limit of $N$-spike string in $AdS_3 \times S^1$ in the presence of flux and show that the so-called Energy-Spin dispersion relation is analogous to the solution we get for the periodic-spike in $AdS_3-pp-$wave $\times S^1$ background with flux.

hep-th↗

arXiv2021

Perturbations of giant magnons and single spikes in $\mathbb R \times S^2$

Perturbations of giant magnons and single spikes in a $2+1$ dimensional $\mathbb R \times S^2$ background spacetime are analysed. Using the form of the giant magnon solution in the Jevicki-Jin gauge,the well-known Jacobi equation for small normal deformations of an embedded time-like surface are written down. Surprisingly, this equation reduces to a simple wave equation in a Minkowski background. The finiteness of perturbations and the ensuing stability of such giant magnons under small deformations are then discussed. It turns out that only the zero mode has finite deformations and is stable. Thereafter, we move on to explore the single spike solution in the Jevicki-Jin gauge. We obtain and solve the perturbation equation numerically and address stability issues.

hep-th↗

arXiv2021

Neumann-Rosochatius system for (m,n) string in $AdS_3 \times S^3$ with mixed flux

$SL(2,\mathbb{Z})$ invariant action for probe $(m,n)$ string in $AdS_3\times S^3\times T^4$ with mixed three-form fluxes can be described by an integrable deformation of an one-dimensional Neumann-Rosochatius (NR) system. We present the deformed features of the integrable model and study general class of rotating and pulsating solutions by solving the integrable equations of motion. For the rotating string, the explicit solutions can be expressed in terms of elliptic functions. We make use of the integrals of motion to find out the scaling relation among conserved charges for the particular case of constant radii solutions. Then we study the closed $(m,n)$ string pulsating in $R_t\times S^3$. We find the string profile and calculate the total energy of such pulsating string in terms of oscillation number $(\cal{N})$ and angular momentum $(\cal{J})$.

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arXiv2020

N spike D-strings in AdS Space with mixed flux

We use Dirac-Born-Infeld action to study the spinning D-string in $AdS_3 $ background in the presence of both NS-NS and RR fluxes. We compute the scaling relation between the energy (E) and spin (S) in the `long string limit'. The energy of these spiky string is found to be a function of spin with the leading logarithmic behaviour and the scaling relation appears to be independent of the amount of flux present. We further discuss folded D-string solutions in $AdS_3$ background with pure NS-NS and R-R fluxes.

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arXiv2020

On finite-size spiky strings in $AdS_3 \times S^3\times T^4$ with mixed fluxes

We discuss finite-size corrections to the spiky strings in $AdS$ space which is dual to the long $\mathcal{N}=4$ SYM operators of the form Tr($Δ_+ ^{J_1}ϕ_1Δ_+ ^{J_2}ϕ_2...Δ_+ ^{J_n}ϕ_n$). We express the finite-size dispersion relation in terms of Lambert $\mathbf{W}$-function. We further establish the finite-size scaling relation between energy and angular momentum of the spiky string in presence of mixed fluxes in terms of $\mathbf{W}$-function. We comment on the solution in pure NS-NS background as well.

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arXiv2019

Neumann-Rosochatius system for strings in ABJ Model

Neumann-Rosochatius system is a well known one dimensional integrable system. We study the rotating and pulsating string in $AdS_4 \times \mathbb{CP}^3$ with a $B_{\rm{NS}}$ holonomy turned on over $\mathbb{CP}^1 \subset \mathbb{CP}^3$, or the so called Aharony-Bergman-Jafferis (ABJ) background. We observe that the string equations of motion in both cases are integrable and the Lagrangians reduce to a form similar to that of deformed Neuman-Rosochatius system. We find out the scaling relations among various conserved charges and comment on the finite size effect for the dyonic giant magnons on $R_{t}\times \mathbb{CP}^{3}$ with two angular momenta. For the pulsating string we derive the energy as function of oscillation number and angular momenta along $\mathbb{CP}^{3}$.

hep-th↗

arXiv2019

On N-spike strings in conformal gauge with NS-NS fluxes

The $AdS_3\times S^3$ string sigma model supported both by NS-NS and R-R fluxes has become a well known integrable model, however a putative dual field theory description remains incomplete. We study the anomalous dimensions of twist operators in this theory via semiclassical string methods. We describe the construction of a multi-cusp closed string in conformal gauge moving in $AdS_3$ with fluxes, which supposedly is dual to a general higher twist operator. After analyzing the string profiles and conserved charges for the string, we find the exact dispersion relation between the charges in the `long' string limit. This dispersion relation in leading order turns out to be similar to the case of pure RR flux, with the coupling being scaled by a factor that depends on the amount of NS-NS flux turned on. We also analyse the case of pure NS flux, where the dispersion relation simplifies considerably. Furthermore, we discuss the implications of these results at length.

hep-th↗

arXiv2019

Finite size effect from classical strings in $AdS_3 \times S^3$ with NS-NS flux

We study the finite size effect of rigidly rotating strings and closed folded strings in $AdS_3\times S^3$ geometry with NS-NS B-field. We calculate the classical exponential corrections to the dispersion relation of infinite size giant magnon and single spike in terms of Lambert $\mathbf{W}-$function. We also write the analytic expression for the dispersion relation of finite size Gubser-Klebanov-Polyakov (GKP) string in the form of Lambert $\mathbf{W}-$function.

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arXiv2018

Perturbations of Pulsating Strings

We discuss semiclassical quantization of circular pulsating strings in AdS3 x S3 background with and without the Neveu-Schwarz- Neveu-Schwarz (NS-NS) flux. We find the equations of motion corresponding to the quadratic action in bosonic sector in terms of scalar quantities and invariants of the geometry. The general equations for studying physical perturbations along the string in an arbitrary curved spacetime are written down using covariant formalism. We discuss the stability of these string configurations by studying the solutions of the linearized perturbed equations of motion.

hep-th↗

arXiv2018

Finite Size Effect from Classical Strings in deformed AdS$_3\times$ S$^3$

We study the finite size effect of rigidly rotating and spinning folded strings in $(AdS_3\times S^3)_{\varkappa}$ background. We calculate the leading order exponential corrections to the infinite size dispersion relation of the giant magnon, and single spike solutions. For the spinning folded strings we write the finite size effect in terms of the known Lambert $W$-function.

hep-th↗

arXiv2018

Perturbations of spiky strings in AdS3

Perturbations of a class of semiclassical spiky strings in three dimensional Anti-de Sitter (AdS) spacetime, are investigated using the well-known Jacobi equations for small, normal deformations of an embedded timelike surface. We show that the equation for the perturbation scalar which governs the behaviour of such small deformations, is a special case of the well-known Darboux-Treibich-Verdier (DTV) equation. The eigenvalues and eigensolutions of the DTV equation for our case are obtained by solving certain continued fractions numerically. These solutions are thereafter utilised to further demonstrate that there do exist finite perturbations of the AdS spiky strings. Our results therefore establish that the spiky string configurations in AdS3 are indeed stable against small fluctuations. Comments on future possibilities of work are included in conclusion.

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