arXiv subjects

Abhishake Sadhukhan

Publications and source records attributed to Abhishake Sadhukhan.

7 recordsLinked to original sources

arXiv2026

Polar-metric/axial-gauge perturbations of the Maldacena-Milekhin-Popov wormhole

We study linear perturbations of the Maldacena-Milekhin-Popov (MMP) traversable wormhole. On a magnetically charged background, polar metric perturbations couple to axial perturbations of the gauge field. We treat this sector and reduce it to two coupled master equations of Zerilli-Moncrief type. The wormhole has two regions. In the mouths the geometry is a nearly extremal magnetic Reissner-Nordstrom black hole with no quantum source. In the throat the Casimir energy of the lowest Landau level of charged fermions holds the wormhole open. We show that the throat equations are consistent only if the fermions respond to the perturbation, computed exactly from the two-dimensional conformal anomaly with the full stress tensor including the trace part that MMP discard. This response must be accompanied by an induced Hall current of the fermions. With both effects included, the linearised Bianchi identities hold at first order in the fermionic backreaction $α$. Deriving the Hall current from the fermion effective action instead requires an Euler term with coefficient $c/48π$, which becomes a coupling between magnetic flux and curvature similar to a Wen-Zee term. At $α=0$ the throat is exact AdS$_2\times S^2$ and the modes decouple into two Poschl-Teller problems with masses $l(l-1)$ and $(l+1)(l+2)$, with levels spaced by $1/\ell$ in frequency. We give the $O(α)$ corrections in closed form. They mix the two modes and depend on frequency, and match the mouths in the overlap region. The symmetric part of the potential is positive throughout the wormhole, excluding purely exponential growth. The corrections lower the normal frequencies and split the levels shared by the two modes, with real shifts at first order in $α$. This sector has no growing mode for $l\ge2$ at this order.

gr-qc↗

arXiv2026

Echoes of the Maldacena-Milekhin-Popov traversable wormhole

We study linear perturbations of massless scalar and vector gauge fields, treated as test fields, on the four-dimensional traversable wormhole of Maldacena, Milekhin, and Popov~\cite{Maldacena:2018gjk}. Both effective potentials vanish throughout the throat and rise in each mouth to a single barrier peaked at the extremal photon-sphere radius $r=2r_e$ for every multipole. In the tortoise coordinate these two barriers are only $\mathcal{O}(10^2)$ wide but sit a distance $2D\simeqπL_{\rm wh}\sim10^{35}$ apart, which puts direct time-domain evolution out of reach. We instead compute the single-barrier scattering amplitudes by Numerov integration, validated against an exactly solvable barrier and against an independent time-domain evolution, and then sum the multiple reflections in closed form. The parabolic WKB formula always gives a transmission probability of $1/2$ at the barrier top, whereas the true value is $0.62$. It also fails below the top, where the transmission falls as $|κ|^2\proptoω^{6.4}$ for $l=1$. Echoes emerge at $T_m=(2m+1)D$ as narrow-band wave packets near the light-ring frequency. Their frequency decreases with each reflection and the energy decays algebraically, $E_m\propto m^{-1}$. The quasinormal spectrum splits into two families. Modes trapped between the barriers are extraordinarily long-lived, with quality factors up to $10^{41}$, and carry the same astronomical time-scale as the echoes. The photon-sphere modes of a single mouth are damped $10^{36}$ times faster than cavity modes, with quality factors of order unity at low multipoles. Only this second family of quasinormal modes is observable, characterising the ringdown of a single mouth. The echoes and the trapped cavity modes instead characterise the late-time dynamics of the throat, not a detectable signal.

gr-qc↗

arXiv2016

Multi-spike strings in $AdS_3$ with mixed three-form fluxes

The string sigma model in $AdS_3\times S^3$ 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 $-\frac{b^2}{2}\log S$. We also discuss the fate of the solution in the limit of pure NS-NS flux.

hep-th↗

arXiv2014

Spinning strings and minimal surfaces in $AdS_3$ with mixed 3-form fluxes

Motivated by the recent proposal for the S-matrix in $AdS_3\times S^3$ with mixed three form fluxes, we study classical folded string spinning in $AdS_3$ with both Ramond and Neveu-Schwarz three form fluxes. We solve the equations of motion of these strings and obtain their dispersion relation to the leading order in the Neveu-Schwarz flux $b$. We show that dispersion relation for the spinning strings with large spin ${\cal S}$ acquires a term given by $-\frac{\sqrtλ}{2π} b^2\log^2 {\cal S}$ in addition to the usual $\frac{\sqrtλ}π \log {\cal S}$ term where $\sqrtλ$ is proportional to the square of the radius of $AdS_3$. Using SO(2,2) transformations and re-parmetrizations we show that these spinning strings can be related to light like Wilson loops in $AdS_3$ with Neveu-Schwarz flux $b$. We observe that the logarithmic divergence in the area of the light like Wilson loop is also deformed by precisely the same coefficient of the $ b^2 \log^2 {\cal S}$ term in the dispersion relation of the spinning string. This result indicates that the coefficient of $ b^2 \log^2 {\cal S}$ has a property similar to the coefficient of the $\log {\cal S}$ term, known as cusp-anomalous dimension, and can possibly be determined to all orders in the coupling $λ$ using the recent proposal for the S-matrix.

hep-th↗

arXiv2013

Structure constants of $β$ deformed super Yang-Mills

We study the structure constants of the ${\cal N}=1$ beta deformed theory perturbatively and at strong coupling. We show that the planar one loop corrections to the structure constants of single trace gauge invariant operators in the scalar sector is determined by the anomalous dimension Hamiltonian. This result implies that 3 point functions of the chiral primaries of the theory do not receive corrections at one loop. We then study the structure constants at strong coupling using the Lunin-Maldacena geometry. We explicitly construct the supergravity mode dual to the chiral primary with three equal U(1) R-charges in the Lunin-Maldacena geometry. We show that the 3 point function of this supergravity mode with semi-classical states representing two other similar chiral primary states but with large U(1) charges to be independent of the beta deformation and identical to that found in the $AdS_5\times S^5$ geometry. This together with the one-loop result indicate that these structure constants are protected by a non-renormalization theorem. We also show that three point function of U(1) R-currents with classical massive strings is proportional to the R-charge carried by the string solution. This is in accordance with the prediction of the R-symmetry Ward identity.

hep-th↗

arXiv2012

Generating string solutions in BTZ

Integrability of classical strings in the BTZ black hole enables the construction and study of classical string propagation in this background. We first apply the dressing method to obtain classical string solutions in the BTZ black hole. We dress time like geodesics in the BTZ black hole and obtain open string solutions which are pinned on the boundary at a single point and whose end points move on time like geodesics. These strings upon regularising their charge and spins have a dispersion relation similar to that of giant magnons. We then dress space like geodesics which start and end on the boundary of the BTZ black hole and obtain minimal surfaces which can penetrate the horizon of the black hole while being pinned at the boundary. Finally we embed the giant gluon solutions in the BTZ background in two different ways. They can be embedded as a spiral which contracts and expands touching the horizon or a spike which originates from the boundary and touches the horizon.

hep-th↗

arXiv2011

Classical integrability in the BTZ black hole

Using the fact the BTZ black hole is a quotient of AdS_3 we show that classical string propagation in the BTZ background is integrable. We construct the flat connection and its monodromy matrix which generates the non-local charges. From examining the general behaviour of the eigen values of the monodromy matrix we determine the set of integral equations which constrain them. These equations imply that each classical solution is characterized by a density function in the complex plane. For classical solutions which correspond to geodesics and winding strings we solve for the eigen values of the monodromy matrix explicitly and show that geodesics correspond to zero density in the complex plane. We solve the integral equations for BMN and magnon like solutions and obtain their dispersion relation. Finally we show that the set of integral equations which constrain the eigen values of the monodromy matrix can be identified with the continuum limit of the Bethe equations of a twisted SL(2, R) spin chain at one loop.

hep-th↗