arXiv subjects

Harvendra Singh

Publications and source records attributed to Harvendra Singh.

At least 19 recordsLinked to original sources

arXiv2025

Exact islands scenario for CFT systems and critical ratios in higher geometry

We study $CFT_d$ systems which are in contact with each other and symmetrically arranged. The system-B is treated as bath that surrounds system-A in the middle. Our focus is to learn how the entanglement entropy of a bath pair system changes as a function of its size. The total size of systems A and B taken together is kept fixed in this process. It is found that for strip shaped systems the bath entropy becomes maximum when respective system sizes follow Fibonacci type critical ratio condition. Beyond critical point when bath size increases the bath entropy starts decreasing, where island and icebergs entropies play important role. Interestingly entire effect of icebergs can be resummed giving rise to 'exact island' scenario for $CFT_d$ with $d>2$. Post criticality we also find important identity involving entropy differences $S[B]-S[A]=S_l-S_{island}$ where island contribution is exact. The mutual information of far separated bath pair follows specific law $I(B:B) \propto {b^2\over (Distance)^d}$. It never vanishes for finite systems. Once system-A size approaches to Kaluza-Klein scale the bath entropy becomes discretized. In summary knowing island corrections is vital for large bath entanglement entropy.

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arXiv2024

Kaluza-Klein discreteness of the entropy: Symmetrical bath and CFT subsystem

We explore the entanglement entropy of CFT systems in contact with large bath system, such that the complete system lives on the boundary of $AdS_{d+1}$ spacetime. We are interested in finding the HEE of a bath (system-B) in contact with a central subsystem-A. We assume that the net size of systems A and B together remains fixed while allowing variation in individual sizes. This assumption is simply guided by the conservation laws. It is found that for large bath size the island entropy term are important. However other subleading (icebergs) terms do also contribute to bath entropy. The contributions are generally not separable from each other and all such contributions add together to give rise a fixed quantity. Further when accounted properly all such contributions will form part of higher entropy branch for the bath. Nevertheless the HEE of bath system should be subjected to minimality principle. The quantum minimality principle $ S_{quantum}[B]=\{S[A], S_{total}+S[A]\}_{min}$, is local in nature and gives rise to the Page curve. It is shown that the changes in bath entropy do capture Kaluza-Klein discreteness. The minimality principle would be applicable in finite temperature systems as well.

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arXiv2024

Islands and Icebergs may contribute nothing to the Page curve

We study the entanglement entropy of a subsystem in contact with symmetrical bath where the complete system lives on the boundary of AdS3 spacetime. The system-A is taken to be in the middle of the bath system-B and the full system is taken to be some fixed localized region of the boundary 2-dimensional CFT. We generally assume that the d.o.f.s in the total system remain fixed when we vary the size of the bath which is to be guided by the conservation laws. It is found that the island and the subleading (icebergs) contributions are inseparable, and in totality they contribute nothing to the Page-curve of the radiation. As such they contribute only to the unphysical branch of the entropy. The entropy formula of the radiation may simply be written as minimum of {S[A],S[B]} including for the black holes.

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arXiv2021

The information horizon entropy for quantum dot and a symmetrical bath

We study the entropy of quantum-dot system in contact with a symmetrical CFT bath living on the boundary of pure AdS3 black hole. The q-dot is localized at the centre of bath system of finite size. We first determine the exact location of the `information horizon' for q-dot and then obtain corresponding generalised entropy of q-dot plus bath system. It is done by finding codim-2 time extremal curve whose end point uniquely determines the information horizon of localised q-dot system. By including the (bulk) entropy contribution of the information horizon the Page curve for the radiation follows. These results can be easily generalized to higher dimensional cases as well.

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arXiv2021

Holography and quantum information exchange between systems

We estimate the net information exchange between adjacent quantum subsystems holographically living on the boundary of $AdS$ spacetime. The information exchange is a real time phenomenon and only after long time interval it may get saturated. Normally we prepare systems for small time intervals and measure the information exchange over finite interval only. We find that the information flow between entangled subsystems gets reduced if systems are in excited state whereas the ground state allows maximum information flow at any given time. Especially for $CFT_2$ we exactly show that a rise in the entropy is detrimental to the information exchange by a quantum dot and vice-versa. We next observe that there is a reduction in circuit (CV) complexity too in the presence of excitations for small times.

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arXiv2021

Entanglement entropy and the first law at third order for boosted black branes

Gauge/gravity duality relates an AdS black hole with uniform boost with a boosted strongly-coupled CFT at finite temperature. We study the perturbative change in holographic entanglement entropy for strip sub-region in such gravity solutions up to third order and try to formulate a first law of entanglement thermodynamics including higher order corrections. The first law receives important contribution from an entanglement chemical potential in presence of boost. We find that suitable modifications to the entanglement temperature and entanglement chemical potential are required to account for higher order corrections. The results can be extended to non-conformal cases and AdS plane wave background.

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arXiv2021

Holographic entanglement entropy for $Lif_4^{(2)}\times {S}^1\times S^5$ spacetime with string excitations

The (F1,D2,D8) brane configuration with $Lif_4^{(2)}\times {S}^1\times S^5$ geometry is a known Lifshitz vacua supported by massive $B_{μν}$ field in type IIA theory. This system allows exact IR excitations which couple to massless modes of the fundamental string. Due to these massless modes the solutions have a flow to a dilatonic $Lif_4^{(3)}\times S^1\times S^5$ vacua in IR. We study the entanglement entropy on the boundary of this spacetime for the strip and the disc subsystems. To our surprise net entropy density of the excitations at first order is found to be independent of the typical size of subsystems. We interpret our results in the light of first law of entanglement thermodynamics.

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arXiv2018

Entanglement entropy at higher orders for the states of a = 3 θ = 1 Lifshitz theory

We evaluate the entanglement entropy of strips for boosted D3-black-branes compactified along the lightcone coordinate. The bulk theory describes $3$-dimensional $a = 3$ $θ = 1$, Lifshitz theory on the boundary. The area of small strips is evaluated perturbatively up to second order, where the leading term has a logarithmic dependence on strip width l, whereas entropy of the excitations is found to be proportional to $l^4$. The entanglement temperature falls off as $\frac{1}{l^3}$ on expected lines. The size of the subsystem has to be bigger than the typical Lifshitz scale in the theory. At second order, the redefinition of temperature(or strip width) is required so as to meaningfully describe the entropy corrections in the form of the first law of entanglement thermodynamics.

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arXiv2018

RG flows and cascades of $Lif_4^{(2)}\times S^1\times S^5$ vacua

The (F1,D2,D8) brane configuration produces $Lif_4^{(2)}\times {S}^1\times S^5$ Lifshitz vacua supported by `massive' $B$-field. We present exact deformations of this system under which new massless $B$-modes of strings also get excited. Due to these massless modes the deformed solutions flow to conformally $Lif_4^{(3)}\times S^1\times S^5$ vacua in the IR. The latter types are supersymmetric solutions of ordinary type IIA theory. The massive and massless $B_{μν}$ modes segregate out in the IR. We confirm that the massive $B$ mode and cosmological constant indeed decouple from the theory rendering the IR field dynamics controlled by massless fields only. A similar effect is observed on the UV side of the flow where a relativistic regime reappears. We also present `cascading' Lifshitz vacua in which dynamical exponent has integral jumps along the flow, $Lif_4^{(3)}\to Lif_4^{(2)}\to Lif_4^{(1)}$. The critical $Lif_4^{(2)}$ theory separates `deconfining' $Lif_4^{(3)}$ IR theory from the confining Yang-Mills phase in UV.

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arXiv2017

Perturbative entanglement thermodynamics for AdS spacetime: Renormalization

We study the effect of charged excitations in the AdS spacetime on the first law of entanglement thermodynamics. It is found that `boosted' AdS black holes give rise to a more general form of first law which includes chemical potential and charge density. To obtain this result we have to resort to a second order perturbative calculation of entanglement entropy for small size subsystems. At first order the form of entanglement law remains unchanged even in the presence of charged excitations. But the thermodynamic quantities have to be appropriately `renormalized' at the second order due to the corrections. We work in the perturbative regime where $T_{thermal}\ll T_E$.

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arXiv2017

Entanglement asymmetry for boosted black branes

We study the effects of asymmetry in entanglement thermodynamics of the CFT subsystems. It is found that `boosted' $p$-branes backgrounds give rise to the first law of the entanglement thermodynamics where the CFT pressure plays decisive role in the entanglement. Two different strip like subsystems, one parallel to the boost and the other perpendicular, are studied in the perturbative regime, where $T_{thermal}\ll T_E$. We also discuss the AdS-wave backgrounds where some universal bounds can be obtained.

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arXiv2017

Instantonic string solitons on M5 branes

The (I)nstantonic strings are described as extended states occupying a flat (isometry) direction on the multiple M5-brane world-volume. These are constituted by 4-dimensional gauge instantons and 2-dimensional chiral axion. In this light we revisit the covariant action for M5-branes by adding explicit axion terms. This leads to a new gauge symmetry and simple modification of some field equations and the constraints in the theory. The equations of motion include a conserved toplological current of I-strings. When 6D theory is compactified on a circle the light-like I-strings manifest as heavy monopole states in 5D super-Yang-Mills. While extremely light I-strings tend to become degenerate with the M5 vacuum but only at strong SYM coupling. This indicates that 6D vacuum is infinitely degenerate.

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arXiv2017

D2-D8 system with massive strings and the Lifshitz spacetimes

The Romans type IIA supergravity allows fundamental strings to have explicit mass term at the tree level. We show that there exists a (F1,D2,D8) brane configuration which gives rise to $Lif_4^{(2)}\times {R}^1\times S^5$ vacua supported by the massive strings. The presence of D8-branes naturally excites massive fundamental strings. A compactification on circle relates these Lifshitz massive type-IIA background with the axion-flux $Lif_4^{(2)}\times {S}^1\times S^5$ vacua in ordinary type-IIB theory. The massive T-duality in eight dimensions further relates them to yet another $\widetilde{Lif}_4^{(2)}\times S^1\times S^5$ vacua constituted by (F1,D0,D6) system in ordinary type IIA theory. The latter vacua after compactification to four dimensions generate two `distinct' electric charges and a constant magnetic field, all living over 2-dimensional plane. This somewhat reminds us of a similar set up in quantum Hall systems.

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arXiv2014

Schrödinger Spacetimes with Screen and Reduced Entanglement

We study a particular class of type II string vacua which become Schrödinger like spacetime in the IR region but are conformally AdS in asymptotic UV region. These solutions are found to possess some unique properties such as the presence of a spacetime `screen'. This Schrödinger (spacetime) screen is however very different from a black-hole horizon. It requires the presence of finite chemical potential and a negative charge density in the Schrödinger CFT. We find that these vacua give rise to reduced entanglement entropy as compared to Lifshitz-AdS counterpart, perhaps due to the screening effects.

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arXiv2014

AdS Bubbles, E$p$-branes and Entanglement

The AdS-bubble solutions interestingly mimic Schrödinger-like geometries when expressed in light-cone coordinates. These D$p$ bubble vacuas exhibit asymmetric scaling property with a negative dynamical exponent of time $a<0$, but are smooth geometries. Through a time-like T-duality we map these vacua to E$p$-brane bubbles with $a>0$ in type II* super-strings. We obtain an expression for the entanglement entropy for `bubble E3-branes'. It is argued that the entropy from E3-bubbles has to be the lowest.

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arXiv2013

Lifshitz to AdS flow with interpolating p-brane solutions

In continuation with our studies of Lifshitz like D$p$-brane solutions, we propose a class of 1/4 BPS supersymmetric interpolating solutions which interpolate between IR Lifshitz solutions and UV AdS solutions smoothly. We demonstrate properties of these classical solutions near the two fixed points. These interpolating solutions are then used to calculate the entanglement entropies of strip-like subsystems. With these bulk solutions the entropy functional also gets modified. We also make a curious observation about the electric-magnetic duality and the thermal entropy of the Hodge-dual Lifshitz D$p$ brane systems.

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arXiv2013

The Yang-Mills and chiral fields in six dimensions

In previous work (Singh, 2011), we constructed an action in six dimensions using Yang-Mills fields and an auxiliary Abelian field. Here we first write down all the equations of motion and the constraints which arise from such an action. From these equations we reproduce all dynamical equations and the constraints required for self-dual tensor field theory constructed by Lambert-Papageorgakis, which describes (2,0) supersymmetric CFT in 6D. This is an indication of the fact that our 6D gauge theory contains all the same information as the on-shall theory of chiral tensor fields.

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arXiv2013

Lifshitz/Schrödinger D-p-branes and dynamical exponents

We extend our earlier study of special double limits of `boosted' $AdS_5$ black hole solutions to include all black D$p$-branes of type II strings. We find that Lifshitz solutions can be obtained in generality, with varied dynamical exponents, by employing these limits. We then study such double limits for `boosted' D$p$-brane bubble solutions and find that the resulting non-relativistic solutions instead describe Schrödinger like spacetimes, having varied dynamical exponents. We get a simple map between these Lifshitz & Schrödinger solutions and a relationship between two types of dynamical exponents. We also discuss about the singularities of the Lifshitz solutions and an intriguing thermodynamic duality.

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