arXiv subjects

Gopal Yadav

Publications and source records attributed to Gopal Yadav.

17 recordsLinked to original sources

arXiv2026

$AdS/CFT$ to $dS/CFT$: Some Recent Developments

These lecture notes aim to provide a pedagogical introduction to the AdS/CFT correspondence and its extensions to spacetimes with positive (de Sitter spacetime) and zero (flat spacetime) cosmological constant. We begin by explaining the physical motivation for holography and the significance of the AdS/CFT correspondence. We then review the basic ingredients of conformal field theory (CFT) and anti de Sitter (AdS) spacetime required to formulate the duality. Building on these foundations, we discuss the formulation of the AdS/CFT correspondence and discuss several consistency checks that support it. We conclude with a brief discussion of holography in de Sitter and flat spacetimes.

hep-th↗

arXiv2025

$dS$ extremal surfaces, replicas, boundary Renyi entropies in $dS/CFT$ and time entanglement

We develop further previous work on de Sitter extremal surfaces and time entanglement structures in quantum mechanics. In the first part, we first discuss explicit quotient geometries. Then we construct smooth bulk geometries with replica boundary conditions at the future boundary and evaluate boundary Renyi entropies in $dS/CFT$. The bulk calculation pertains to the semiclassical de Sitter Wavefunction and thus evaluates pseudo-Renyi entropies. In 3-dimensions, the geometry in quotient variables is Schwarzschild de Sitter. The 4-dim $dS$ geometry involves hyperbolic foliations and is a complex geometry satisfying a regularity criterion that amounts to requiring a smooth Euclidean continuation. Overall this puts on a firmer footing previous Lewkowycz-Maldacena replica arguments based on analytic continuation for the extremal surface areas via appropriate cosmic branes. In the second part (independent of de Sitter), we study various aspects of time entanglement in quantum mechanics, in particular the reduced time evolution operator, weak values of operators localized to subregions, a transition matrix operator with two copies of the time evolution operator, autocorrelation functions for operators localized to subregions, and finally future-past entangled states and factorization. Based on these, we then give some comments on a cosmological transition matrix using the de Sitter Wavefunction.

hep-th↗

arXiv2024

No-boundary extremal surfaces in slow-roll inflation and other cosmologies

Building on previous work on de Sitter extremal surfaces anchored at the future boundary, we study no-boundary extremal surfaces in slow-roll inflation models, with perturbations to no-boundary global $dS$ preserving the spatial isometry. While in pure de Sitter space the Euclidean hemisphere gives a real area equalling half de Sitter entropy, the no-boundary extremal surface areas here have nontrivial real and imaginary pieces overall. We evaluate the area integrals in the complex time-plane defining appropriate contours. For the 4-dim case, the real and imaginary finite corrections at leading order in the slow-roll parameter match those in the semiclassical expansion of the Wavefunction (or action), and corroborate the cosmic brane interpretation discussed previously. We also study no-boundary extremal surfaces in other cosmologies including 3-dimensional inflation and Schwarzschild de Sitter spaces with small mass.

hep-th↗

arXiv2024

Cosmological singularities, holographic complexity and entanglement

We study holographic volume complexity for various families of holographic cosmologies with Kasner-like singularities, in particular with $AdS$, hyperscaling violating and Lifshitz asymptotics. We find through extensive numerical studies that the complexity surface always bends in the direction away from the singularity and transitions from spacelike near the boundary to lightlike in the interior. As the boundary anchoring time slice approaches the singularity, the transition to lightlike is more rapid, with the spacelike part shrinking. The complexity functional has vanishing contributions from the lightlike region so in the vicinity of the singularity, complexity is vanishingly small, indicating a dual Kasner state of vanishingly low complexity, suggesting an extreme thinning of the effective degrees of freedom dual to the near singularity region. We also develop further previous studies on extremal surfaces for holographic entanglement entropy, and find that in the IR limit they reveal similar behaviour as complexity.

hep-th↗

arXiv2024

Communicating multiverses in a holographic de Sitter braneworld

In this paper, we construct the wedge holography for the de-Sitter space as a bulk theory. First, we discuss a more general mathematical construction of wedge holography in parallel with wedge holography construction for the AdS bulk, and then we construct the wedge holography in the extended static patch. In the first case, we prove that one can construct wedge holography for the de-Sitter bulk for the static patch as well as global coordinate metric on end-of-the-world branes. Extended static patch wedge holography is constructed by joining the two copies of double holography in DS/dS correspondence. We find that wedge holography with extended static patch metric leads to the emergence of communicating universes. Further, we propose a model which provides the theoretical evidence of communicating multiverses.

hep-th↗

arXiv2023

Pole-Skipping and Chaos in Hot ${\cal M}$QCD

We address the question of whether thermal QCD at high temperature is chaotic from the ${\cal M}$ theory dual of QCD-like theories at intermediate coupling as constructed in arXiv: 2004.07259. The equations of motion of the gauge-invariant combination $Z_s(r)$ of scalar metric perturbations is shown to possess an irregular singular point at the horizon radius $r_h$. Very interestingly, at a specific value of the imaginary frequency and momentum used to read off the analogs of the ''Lyapunov exponent'' $\lambda_L$ and ''butterfly velocity'' $v_b$ not only does $r_h$ become a regular singular point, but truncating the incoming mode solution of $Z_s(r)$ as a power series around $r_h$, yields a ''missing pole'', i.e., $C_{n, n+1}=0,\ {\rm det}\ M^{(n)}=0, n\in\mathbb{Z}^+$ is satisfied for a single $n\geq3$ depending on the values of the string coupling $g_s$, number of (fractional) $D3$ branes $(M)N$ and flavor $D7$-branes $N_f$ in the parent type IIB set (arXiv:hep-th/0902.1540), e.g., for the QCD(EW-scale)-inspired $N=100, M=N_f=3, g_s=0.1$, one finds a missing pole at $n=3$. For integral $n>3$, truncating $Z_s(r)$ at ${\cal O}((r-r_h)^n)$, yields $C_{n, n+1}=0$ at order $n,\ \forall n\geq3$. Incredibly, (assuming preservation of isotropy in $\mathbb{R}^3$ even with the inclusion of higher derivative corrections) the aforementioned gauge-invariant combination of scalar metric perturbations receives no ${\cal O}(R^4)$ corrections. Hence, (the aforementioned analogs of) $\lambda_L, v_b$ are unrenormalized up to ${\cal O}(R^4)$ in ${\cal M}$ theory.

hep-th↗

arXiv2023

Aspects of Thermal QCD Phenomenology at Intermediate Gauge/'t Hooft Coupling from String/M-Theory, (HD) Gravity Islands, and Multiverse

As applications of arXiv:2004.07259, the first part of the thesis is based on (i) arXiv:2011.04660 wherein we computed the low energy coupling constants of SU(3) chiral perturbation theory at NLO in the chiral expansion in the chiral limit, from the type IIA string dual inclusive of ${\cal O}(R^4)$ corrections and found a novel HD-large-$N$ connection; (ii) arXiv:2108.05372, arXiv:2203.11959 wherein we discussed confinement-deconfinement phase transition in thermal QCD-like theories at intermediate coupling in the absence/presence of rotation and observed (a) a novel "UV-IR" mixing, (b) "Flavor Memory" effect, (c) M$\chi$PT compatibility,(d) non-renormalization of deconfinement temperature $T_c$ beyond one loop in the zero instanton sector, and (e) found that the $T_c$ of rotating QGP decreases when angular velocity of rotating cylindrical black hole increases and vice-versa. In the second part of thesis, we obtained Page curves of Reissner-Nordstr\"{o}m black holes in the presence of ${\cal O}(R^2)$ terms and black holes with multiple horizons in arXiv:2204.11882 and arXiv:2210.00331 respectively. In arXiv:2207.04048, we constructed a doubly holographic setup for a non-conformal bath (thermal QCD) in ${\cal M}$-theory background with the inclusion of ${\cal O}(R^4)$ terms and obtained the Page curve of an eternal neutral black hole for massless graviton localized on an ETW-"brane"/(Fluxed) hypersurface. Multiverse is described as the setup of 2n anti de-Sitter (AdS) or de-Sitter branes embedded in the corresponding bulk (arXiv:2301.06151). Since all the universes can communicate with each other due to transparent boundary conditions at the defect, therefore one could exchange information between any universes. This setup is also used to obtain the Page curve of the Schwarzschild de-Sitter black hole, which has two horizons.

hep-th↗

arXiv2023

QCD-Compatible Supermassive Inert Top-Down Holographic Mesinos at Intermediate Coupling

A longstanding problem with the popular Sakai-Sugimoto holographic dual of thermal QCD is that the "mesinos", the (non-supersymmetric) fermionic partners of the mesons, are nearly isospectral with mesons and have an unsuppressed mesino-meson interaction, both being in contradiction with actual QCD. We solve this problem in a UV-complete (and ${\it different}$) type IIA string dual ${\it at\ intermediate\ coupling}$ of realistic thermal QCD, in which the mesinos are shown to be much heavier than and non-interacting with mesons (the wave-function/mass/interaction terms receiving no ${\cal M}$-theory ${\cal O}(R^4)$ corrections). In particular we derive a large-$N$ enhancement of the KK mass scale $M_{KK}$ (from $M_{KK}$ to $M_{KK}^{\rm eff}\sim N^{1 + \frac{1}{{\cal O}(1)}}M_{KK}$) arising from the construction of the type IIA mirror \cite{MQGP} of the type IIB dual \cite{metrics} of thermal QCD-like theories, as well as the generation of a one-parameter family of $M_{KK}$-independent mass scale at ${\cal O}(R^4)$ in the ${\cal M}$-theory uplift \cite{OR4} wherein the parameter can be made appropriately large. We also show that the mesino-mesino-single-($\rho/\pi$)meson interactions, vanish identically in the aforementioned type IIA holographic dual.

hep-th↗

arXiv2023

Yang-Baxter deformed wedge holography

In this paper, we construct the wedge holography in the presence of homogeneous Yang-Baxter deformation. We observe that the DGP term is the reason for the existence of non-zero tension of the Karch-Randall branes in Yang-Baxter deformed wedge holography. The homogeneous Yang-Baxter deformation introduce non-trivial island surfaces inside the black hole horizon whose entanglement entropy is lower than the twice of thermal entropy of the black hole. Therefore, we obtain the Page curve even without the DGP term on the Karch-Randall branes due to the homogeneous Yang-Baxter deformation in the context of wedge holography. Finally, we compute the the holographic complexity in homogeneous Yang-Baxter deformed $AdS_2$ background.

hep-th↗

arXiv2023

Multiverse in Karch-Randall Braneworld

In this paper, we propose a model based on wedge holography that can describe the multiverse. In wedge holography, we consider two gravitating baths, one of which has strong gravity and the other one has weak gravity. To describe a multiverse, we consider $2n$ Karch-Randall branes, and we propose that various $d$-dimensional universes are localized on these branes. These branes are embedded in $(d+1)$-dimensional spacetime. The model is useful in obtaining the Page curve of black holes with multiple horizons and in the resolution of the ``grandfather paradox''. We explicitly obtain the Page curves of eternal AdS black holes for $n=2$ multiverse and Schwarzschild de-Sitter black hole with two horizons.

hep-th↗

arXiv2022

On the Ubiquity of (Almost) Contact Structures in Hot MQCD at Intermediate Coupling

Relevant to top-down ${\cal M}$-theory dual of large-$N$ thermal QCD-like theories at intermediate coupling, induced by the $G_2$ structure supported by the closed $M_7$ - a warped product of the ${\cal M}$-theory circle and a non-K\"{a}hler six-fold which is the warped product of the thermal circle with a non-Einsteinian deformation of $T^{1,1}$ - we obtain explicitly (Almost) Contact (3) (Metric)Structure(s) and a three-tuple of $SU(3)$ structures along the "transverse" six-fold induced by the AC(3)MS on $M_7$. A novel result in this context is that in the Infra-Red, within the parameter space of AC3S arising from G2 structures, the subspaces of C3S and AC3S are not mutually "N-path connected". Relevance of the results to staying out of the non-supersymmetric swampland, entanglement entropy of eternal black holes, chaos, bulk-to-shear viscosity ratio $\frac{\zeta}{\eta}$, paramagnetic plasma EoS and photoproduction in a strong magnetic field, in the context of top-down holographic thermal QCD at intermediate coupling, is highlighted/reiterated.

hep-th↗

arXiv2022

Cosmological and black hole islands in multi-event horizon spacetimes

In this paper, we have analyzed the information paradox and its resolution using island proposal in Schwarzschild de-Sitter black hole spacetime. First, we study the information paradox for the black hole patch by treating de-Sitter patch on both sides as a frozen background (by inserting thermal opaque membrane) and then we carry out similar study for de-Sitter patch also. In both cases, when there is no island surface then the entanglement entropy has as usual the linear time dependence whereas in the presence of an island surface entanglement entropy become constant (equal to twice of thermal entropy of black hole/de-Sitter patch). Therefore, we obtain the Page curves for the black hole and de-Sitter patch consistent with the unitary evolution of black holes. In our case, we have found that black hole island is located inside the black hole event horizon in contrast to universal result for eternal black holes and also cosmological island is located inside the cosmological event horizon. Further, we have studied the "effect of temperature" on the Page curves and found that Page curves appear at later times for low temperature black holes/de-Sitter patch and it exhibit opposite behavior for high temperature. This implies that "dominance of islands" and "information recovery" takes more time for low temperature black holes/de-Sitter patch in contrast to high temperature black holes/de-Sitter patch. We also make comments on the challenges to study the information paradox in SdS spacetime without the thermal opaque membrane.

hep-th↗

arXiv2022

Entanglement entropy and Page curve from the ${\cal M}$-theory dual of thermal QCD above $T_c$ at intermediate coupling

Obtaining the Page curve in the context of eternal black holes associated with top-down non-conformal holographic thermal duals at intermediate coupling, has been entirely unexplored in the literature. We fill this gap in the context of a doubly holographic setup relevant to the M-theory dual of thermal QCD-like theories at $T>T_c$ at intermediate coupling. Remarkably, excluding the higher derivative terms, the entanglement entropy(EE) of the Hawking radiation from the on-shell Wald EE (for appropriate choices of constants of integration appearing in the embeddings) increases almost linearly with the boundary time due to dominance of EE contribution from the Hartman-Maldacena(HM)-like surface $S_{EE}^{HM, \beta^0}, \beta\sim l_p^6$. Curiously, this imparts a "Swiss-Cheese" structure to the surface $S_{EE}^{HM, \beta^0}$ at a given time (less than the Page time $t_{P}$), in $\mathbb{R}_{\geq0} \times \mathbb{C}$ effecting what could be dubbed as a "Large N Scenario" (LNS). Then, after $t_{P}$, the EE contribution from the Island Surface (IS) $S_{EE}^{IS, \beta^0}$ dominates and saturates the linear time growth of the EE of Hawking radiation and leads to the Page curve. Requiring $S_{EE}^{IS, \beta^0}/S_{BH}\sim2$ up to LO in the non-conformal analog of "$c G_N^{(11)}/r_h^9$", and positivity of $t_{P}$, set respectively a lower and upper bound on the horizon radius $r_h$ (the non-extremality parameter). With the inclusion of the $O(R^4)$ terms in M theory, the turning point associated with the HM-like surface/IS being in the deep IR, results in a relationship between $l_p$ and $r_h$ along with a conjectural $e^{-{\cal O}(1) N^{1/3}}$-suppression (motivated by $S_{EE}^{IS, \beta^0}/S_{BH}\sim2$). We obtain a hierarchy with respect to this N-dependent exponential in $S_{EE}^{HM, \beta^0}, S_{EE}^{IS, \beta^0} (O(\beta^0))$ and $S_{EE}^{HM, \beta}, S_{EE}^{HM, \beta} (O(\beta))$.

hep-th↗

arXiv2022

Page Curves of Reissner-Nordstr\"om Black Hole in HD Gravity

We obtain the Page curves of an eternal Reissner-Nordstr\"om black hole in the presence of higher derivative terms in four dimensions. We consider two cases: gravitational action with general ${\cal O}(R^2)$ terms plus Maxwell term and Einstein-Gauss-Bonnet gravity plus Maxwell term. In both the cases entanglement entropy of the Hawking radiation in the absence of island surface is increasing linearly with time. After including contribution from the island surface, we find that after the Page time, entanglement entropy of the Hawking radiation in both the cases reaches a constant value which is the twice of the Bekenstein-Hawking entropy of the black hole and we obtain the Page curves. We find that Page curves appear at later or earlier time when the Gauss-Bonnet coupling increases or decreases. Further, scrambling time of Reissner-Nordstr\"om is increasing or decreasing depending upon whether the correction term (coming from ${\cal O}(R^2)$ terms in the gravitational action) is increasing or decreasing in the first case whereas scrambling time remains unaffected in the second case (Einstein-Gauss-Bonnet gravity case). As a consistency check, in the limit of vanishing GB coupling we obtain the Page curve of the Reissner-Nordstr\"om black hole obtained in arXiv:2101.06867.

hep-th↗

arXiv2022

Deconfinement Temperature of Rotating QGP at Intermediate Coupling from ${\cal M}$-Theory

With the aim of studying rotating quark-gluon plasma (QGP), holographically, from a top-down approach, the study of the effect of rotation on the deconfinement temperature of thermal QCD-like theories at intermediate coupling from ${\cal M}$-theory was missing in the literature. This paper fills this gap. The gravity dual includes a rotating cylindrical black hole. In the presence of rotation, from a semi-classical computation, we found that the deconfinement temperature is inversely proportional to the Lorentz factor, which suggests that the deconfinement temperature decreases with the increase of rotation. Further, we found that in the small angular velocity limit, results from higher derivative correction at ${\cal O}(R^4)$ do not change and are the same as in arXiv:2108.05372. The "UV-IR mixing", "Flavor Memory" effect, and "non-renormalization of $T_c$" in the ${\cal M}$-theory dual are similar to the ones observed in arXiv:2108.05372.

hep-th↗

arXiv2021

${\mathscr {M}}$cTEQ (${\mathscr {M}}$ ${\bf c}$hiral perturbation theory-compatible deconfinement ${\bf T}$emperature and ${\bf E}$ntanglement Entropy up to terms ${\bf Q}$uartic in curvature) and FM (${\bf F}$lavor ${\bf M}$emory)

A holographic computation of $T_c$ at ${\it intermediate\ coupling}$ from M-theory dual of thermal QCD-like theories, has been missing in the literature. Filling this gap, we demonstrate a novel UV-IR mixing, (conjecture and provide evidence for) a non-renormalization beyond 1 loop of ${\bf M}-{\bf c}$hiral perturbation theory arXiv:2011.04660[hep-th]-compatible deconfinement ${\bf T}$emperature, and show equivalence with an ${\bf E}$ntanglement (as well as Wald) entropy arXiv:0709.2140[hep-th] computation, up to terms ${\bf Q}$uartic in curvature. We demonstrate a ${\bf F}$lavor-${\bf M}$emory (FM) effect in the M-theory uplifts of the gravity duals, wherein the no-braner M-theory uplift retains the "memory" of the flavor D7-branes of the parent type IIB dual in the sense that a specific combination of the aforementioned quartic corrections to the metric components precisely along the compact part of the non-compact four-cycle "wrapped" by the flavor D7-branes, is what determines, e.g., the Einstein-Hilbert action at O$(R^4)$. The same linear combination of O$(R^4)$ metric corrections, upon matching the phenomenological value of the coupling constant of one of the SU(3) NLO ChPT Lagrangian, is required to have a definite sign. Interestingly, in the decompactification limit of the spatial circle, we ${\it derive}$ this, and obtain the values of the relevant O$(R^4)$ metric corrections. Further, equivalence with Wald entropy for the black hole at ${\cal O}(R^4)$ imposes a linear constraint on the same linear combination of metric corrections. Remarkably, when evaluating $T_c$ from an entanglement entropy computation in the thermal gravity dual, due to a delicate cancelation between the ${\cal O}(R^4)$ corrections from a subset of the abovementioned metric components, one sees that there are no corrections to $T_c$ at quartic order supporting the conjecture referred to above.

hep-th↗

arXiv2021

(Phenomenology/Lattice-Compatible) $SU(3)$ M$χ$PT HD up to ${\cal O}(p^4)$ and the ${\cal O}\left(R^4\right)$-Large-$N$ Connection

Obtaining the values of the coupling constants of the low energy effective theory corresponding to QCD, compatible with experimental data, even in the (vector) mesonic sector from (the ${\cal M}$-theory uplift of) a UV-complete string theory dual, has thus far been missing in the literature. We take the first step in this direction by obtaining the values of the coupling constants of the ${\cal O}(p^4)$ $χ$PT Lagrangian in the chiral limit involving the NGBs and $ρ$ meson (and its flavor partners) from the ${\cal M}$-theory /type IIA dual of large-$N$ thermal QCD, inclusive of the ${\cal O}(R^4)$ corrections. We observe that ensuring compatibility with phenomenological/lattice results (the values ) as given in arXiv:1510.01634[hep-ph], requires a relationship relating the ${\cal O}(R^4)$ corrections and large-$N$ suppression. In other words, QCD demands that the higher derivative corrections and the large-$N$ suppressed corrections in its M/string theory dual are related. As a bonus, we explicitly show that the ${\cal O}(R^4)$ corrections in the UV to the ${\cal M}$-theory uplift of the type IIB dual of large-$N$ thermal QCD, can be consistently set to be vanishingly small.

hep-th↗