In this paper we study the thermodynamics of black branes at quantum scales. We analyze both perturbative and non-perturbative corrections to the thermodynamics of such black branes. It will be observed that these corrections will modify the relation between the entropy and area of these black branes. This will in turn modify their specific heat, and thus their stability. So, such corrections can have important consequences for the stability of black branes at quantum scales. We also analyze the effect of these perturbative and non-perturbative quantum corrections on various other thermodynamic quantities. Then, we obtain the metric for the quantum corrected geometry for black branes.
Introductory lectures on the relations between the thermodynamics of gauge theory on branes and black holes, including the correspondence principle of Horowitz and Polchinski, the AdS/CFT conjecture, and matrix theory.
We show that the correct entropy, temperature (and absorption probability) of non-extremal black p-brane can be reproduced by a certain thermodynamical model when maximizing its entropy. We show that the form of the model is related to the geometrical similarity of non-extremal and near extremal black p-brane at near horizon region, and argue about the appropriateness of the model.
We discuss general spinning p-branes of string and M-theory and use their thermodynamics along with the correspondence between near-horizon brane solutions and field theories with 16 supercharges to describe the thermodynamic behavior of these theories in the presence of voltages under the R-symmetry. The thermodynamics is used to provide two pieces of evidence in favor of a smooth interpolation function between the free energy at weak and strong coupling of the field theory. (i) A computation of the boundaries of stability shows that for the D2, D3, D4, M2 and M5-branes the critical values of…
Thermodynamic properties of a class of black $p$-branes in $D$-dimensions considered by Duff and Lu are investigated semi-classically. For black $(d-1)$-brane, thermodynamic quantities depend on $D$ and $d$ only through the combination $\tilde d \equiv D-d-2$. The behavior of the Hawking temperature and the lifetime vary with $\tilde d$, with a critical value $\tilde d=2$. For $\tilde d>2$, there remains a remnant, in which non-zero entropy is stored. Implications of the fact that the Bekenstein-Hawking entropy of the black $(d-1)$-brane depend only on $\tilde d=D-d-2$ is discussed from the po…
We consider the thermodynamics of the near-extremal NS5-brane in type IIA string theory. The central tool we use is to map phases of six-dimensional Kaluza-Klein black holes to phases of near-extremal M5-branes with a transverse circle in eleven-dimensional supergravity. By S-duality these phases correspond to phases of the near-extremal type IIA NS5-brane. One of our main results is that in the canonical ensemble the usual near-extremal NS5-brane background, dual to a uniformly smeared near-extremal M5-brane, is subdominant to a new background of near-extremal M5-branes localized on the trans…
We derive the generalized Friedmann equation governing the cosmological evolution inside the thick brane model in the presence of two curvature correction terms: a four-dimensional scalar curvature from induced gravity on the brane, and a five-dimensional Gauss-Bonnet curvature term. We find two effective four-dimensional reductions of the Friedmann equation in some limits and demonstrate that they can be rewritten as the first law of thermodynamics on the apparent horizon of thick braneworld.
Thermodynamic properties of Schwarzschild-Anti de-Sitter (Sch-AdS) and Reissner-Nordström-Anti de-Sitter (RN-AdS) blackholes in 3+1 dimensional spacetime are studied critically with special reference to the warped braneworld black holes with non-vanishing cosmological constant on the brane. Explicit dependence of the thermodynamic variables on the parameters of the braneworld model such as the induced three brane cosmological constant as well as the bulk cosmological constant have been determined. Hawking-Page phase transition has been discussed for both Sch-AdS and RN-AdS black holes. At the …
We consider the thermodynamic and cosmological properties of brane gases in the early universe. Working in the low energy limit of M-theory we assume the universe is a homogeneous but anisotropic 10-torus containing wrapped 2-branes and a supergravity gas. We describe the thermodynamics of this system and estimate a Hagedorn temperature associated with excitations on the branes. We investigate the cross-section for production of branes from the thermal bath and derive Boltzmann equations governing the number of wrapped branes. A brane gas may lead to decompactification of three spatial dimensi…
The holographic dual of a finite-temperature gauge theory with a small number of flavours typically contains D-brane probes in a black hole background. We have recently shown that these systems undergo a first order phase transition characterised by a `melting' of the mesons. Here we extend our analysis of the thermodynamics of these systems by computing their free energy, entropy and energy densities, as well as the speed of sound. We also compute the meson spectrum for brane embeddings outside the horizon and find that tachyonic modes appear where this phase is expected to be unstable from t…
We consider the brane universe in the bulk background of the topological Reissner-Nordström de Sitter black holes. We show that the thermodynamic quantities (including entropy) of the dual CFT take usual special forms expressed in terms of Hubble parameter and its time derivative at the moment, when the brane crosses the black hole horizon or the cosmological horizon. We obtain the generalized Cardy-Verlinde formula for the CFT with an charge and cosmological constant, for any values of the curvature parameter $k$ in the Friedmann equations.
We study the dynamics and thermodynamics of a probe D3-brane in the rotating D3-brane background and in its extremal limit, which is a multicenter configuration of D3-branes distributed uniformly on a disc. In the extremal background, if the angular momentum of the probe does not vanish, the probe is always bounced back at some turning point. When its angular momentum vanishes, in the disc plane, the probe will be captured at the edge of the disc; in the hyperplane orthogonal to the disc, the probe will be absorbed at the center of the disc. In the non-extremal background, if the probe is in t…
We examine the matrix theory representation of D0-brane dynamics at finite temperature. In this case, violation of supersymmetry by temperature leads to a non-trivial static potential between D0-branes at any finite temperature. We compute the static potential in the 1-loop approximation and show that it is short-ranged and attractive. We compare the result with the computations in superstring theory. We show that thermal states of D0-branes can be reproduced by matrix theory only when certain care is taken in integration over the moduli space of classical solutions in compactified time.
Spinning black three-branes in type IIB supergravity are thermodynamically stable up to a critical value of the angular momentum density. Inside the region of thermodynamic stability, the free energy from supergravity is roughly reproduced by a naive model based on free N=4 super-Yang-Mills theory on the world-volume. The field theory model correctly predicts a limit on angular momentum density, but near this limit it does not reproduce the critical exponents one can compute from supergravity. Analogies with Bose condensation and modified matrix models are discussed, and a mean field theory im…
We discuss the dynamics and thermodynamics of particle and D-brane probes moving in non-extremal black hole/brane backgrounds. When a probe falls from asymptotic infinity to the horizon, it transforms its potential energy into heat, $TdS$, which is absorbed by the black hole in a way consistent with the first law of thermodynamics. We show that the same remains true in the near-horizon limit, for BPS probes only, with the BPS probe moving from AdS infinity to the horizon. This is a quantitative indication that the brane-probe reaching the horizon corresponds to thermalization in gauge theory. …
We determine the thermodynamic stability conditions for near-extreme rotating D3, M5, and M2-branes with multiple angular momenta. Critical exponents near the boundary of stability are discussed and compared with a naive field theory model. From a partially numerical computation we conclude that outside the boundary of stability, the angular momentum density tends to become spatially inhomogeneous. Periodic Euclidean spinning brane solutions have been studied as models of QCD. We explain how supersymmetry is restored in the world-volume field theory in the limit of large spin and discuss the h…
We construct a class of charged rotating solutions in $(n+1)$-dimensional Maxwell-Brans-Dicke theory with flat horizon in the presence of a quadratic potential and investigate their properties. These solutions are neither asymptotically flat nor (anti)-de Sitter. We find that these solutions can present black brane, with inner and outer event horizons, an extreme black brane or a naked singularity provided the parameters of the solutions are chosen suitably. We compute the finite Euclidean action through the use of counterterm method, and obtain the conserved and thermodynamic quantities by us…
We consider asymptotically AdS black brane solutions that are dual to CFTs with periodic dependence on the spatial directions, arising from either a spontaneous or an explicit breaking of translational symmetry. We derive a simple expression for the variation of the free-energy with respect to changing the periods. This explains some observations, based on numerics, that have arisen in the explicit construction of thermodynamically preferred black holes in the case that the spatial directions are infinite in extent and the symmetry is spontaneously broken. It also leads to simple Smarr-type re…
A certain sector of the matrix model for M-theory on a plane wave background has recently been shown to produce the transverse five-brane. We consider this theory at finite temperature. We find that, at a critical temperature it has a Gross-Witten phase transition which corresponds to deconfinement of the matrix model gauge theory. We interpret the phase transition as the Hagedorn transition of M-theory and of type II string theory in the five-brane background. We also show that there is no Hagedorn behaviour in the transverse membrane background case.
We study the thermodynamics of open superstrings in the presence of $p$-dimensional D-branes. We get some finite temperature dualities relating the one-loop canonical free energy of open strings to the self-energy of D-branes at dual temperature. For the open bosonic string the inverse dual temperature is, as expected, the dual length under T-duality, $4π^{2}α^{'}/β$. On the contrary, for the $SO(N)$, type-I superstring the dual temperature is given by $β$-duality, $2π^{2}α^{'}/β$. We also study the emergence of the Hagedorn singularity in the dual description as triggered by the coupling of t…
Recently, a class of gravitational backgrounds in 3+1 dimensions have been proposed as holographic duals to a Lifshitz theory describing critical phenomena in 2+1 dimensions with critical exponent $z\geq 1$. We continue our earlier work \cite{Bertoldi:2009vn}, exploring the thermodynamic properties of the "black brane" solutions with horizon topology $\mathbb{R}^2$. We find that the black branes satisfy the relation $\mathcal{E}=\frac{2}{2+z}Ts$ where $\mathcal{E}$ is the energy density, $T$ is the temperature, and $s$ is the entropy density. This matches the expected behavior for a 2+1 dimens…
Curvature-squared corrections for D-brane actions in type II string theory were derived by Bachas, Bain and Green. Here we write down a generalisation of these corrections to all orders in $F$, the field strength of the U(1) gauge field on the brane. Some of these terms are needed to restore consistency with T-duality.
If an Einstein-Maxwell-Dilaton system admits the extreme brane solution in which no force works between the parallel branes, the collective motion of nearly parallel branes exhibits the thermodynamical properties which are coincident with those of the corresponding black branes at low energy regime (up to unfixed numerical factors). Hence it may provide the microscopic description of the black branes ($p$-soup proposal). This fact motivates us to test this proposal in the intersecting black branes which have multiple brane charges and/or momentum along the brane direction. We consider the case…
We construct a new class of charged rotating solutions of $(n+1)$-dimensional Einstein-Born-Infeld gravity with cylindrical or toroidal horizons in the presence of cosmological constant and investigate their properties. These solutions are asymptotically (anti)-de Sitter and reduce to the solutions of Einstein-Maxwell gravity as the Born-Infeld parameters goes to infinity. We find that these solutions can represent black branes, with inner and outer event horizons, an extreme black brane or a naked singularity provided the parameters of the solutions are chosen suitably. We compute temperature…
We will investigate a system of M2-M5 branes as a black M2-M5 bound state. The behavior of this system will be investigated at short distances. At such scales, we will have to incorporate quantum gravitational corrections to the supergravity solutions. We will study the non-equilibrium quantum thermodynamics of this black M2-M5 bound state. The quantum work for this solution will be obtained using the Jarzynski equality. We will also study the corrections to the thermodynamic stability of this system from quantum gravitational corrections. We will use the concept of a novel quantum mass to ana…
We study worldsheet instanton corrections to the exotic 522-brane geometry in type II string theory. The BPS vortices in the N=(4,4) gauged linear sigma model modify the geometry of the 522-brane. We find that the modification of the geometry is understood by the localization in the T-dualized winding direction.
The thermodynamics and phase transitions of charged RN-AdS and rotating Kerr-AdS black holes in a generalized Randall-Sundrum braneworld are investigated in the framework of thermodynamic geometry. A detailed analysis of the thermodynamics, stability and phase structures in the canonical and the grand canonical ensembles for these AdS braneworld black holes are described. The thermodynamic curvatures for both these AdS braneworld black holes are computed and studied as a function of the thermodynamic variables. Through this analysis we illustrate an interesting dependence of the phase structur…
Following the conjectured duality between near-horizon NS5-branes and little string theory, the string-corrected thermodynamics of near-horizon NS5-branes is studied and found to agree with the statistical thermodynamics of a 5+1 dimensional supersymmetric string theory near the Hagedorn temperature. Specifically, tree-level corrections to the temperature are argued to vanish, in accordance with the duality, while the one-loop string correction to the NS5-brane thermodynamics is shown to generate the correct temperature dependence of the entropy.
Like BPS D3 brane, the non-supersymmetric (non-susy) D3 brane of type IIB string theory is also known to have a decoupling limit and leads to a non-supersymmetric AdS/CFT correspondence. The throat geometry in this case represents a QFT which is neither conformal nor supersymmetric. The `black' version of the non-susy D3 brane in the decoupling limit describes a QFT at finite temperature. Here we first compute the entanglement entropy for small subsystem of such QFT from the decoupled geometry of `black' non-susy D3 brane using holographic technique. Then we study the entanglement thermodynami…
We consider a $σ$-model formulation of open string theory in the presence of D-branes. We perform two-loop computations and discuss gravitational corrections to Born-Infeld action when branes are non-trivially embedded in a curved ambient space. In particular for the case of a stack of $N$ coincident D-branes we analyze couplings of the form $R_{ijkl}[Φ^i,Φ^j][Φ^k,Φ^l]$.
We study dynamics of a cosmic string in a metastable brane configuration in Type IIA string theory. We first discuss a decay process of the cosmic string via a fuzzy brane (equivalently bubble/string bound state) by neglecting gravitational corrections in ten-dimension. We find that depending on the strength of the magnetic field induced on the bubble, the decay rate can be either larger or smaller than that of $O(4)$ symmetric bubble. Then, we investigate gravitational corrections to the fuzzy brane by using the extremal black $NS$-five brane solution, which makes the lifetime of the metastab…
We calculate the one-loop corrections to gauge couplings in N=1 supersymmetric brane world models, which are realized in an type IIA orbifold/orientifold background with several stacks of D6 branes wrapped on 3-cycles with non-vanishing intersections. Contributions arise from both N=1 and N=2 open string subsectors. In contrast to what is known from ordinary orbifold theories, N=1 subsectors give rise to moduli-dependent one-loop corrections.
In our previous work (Phys. Rev. D63, 085010, hep-th/0011290), we showed that the brane universe on the giant graviton moving in the near-horizon background of the dilatonic D(6-p)-brane is described by the mirage cosmology. We study thermodynamic properties of the moving giant graviton by applying thermodynamics of cosmology and the recently proposed holographic principles of cosmology. We find that the Fischler-Susskind holographic bound is satisfied by the closed brane universe on the moving giant graviton with p>3. The Bekenstein and the Hubble entropy bounds and the recently proposed Verl…
We dimensionally reduce the four-derivative corrections to the parity-conserving part of the D9-brane effective action involving all orders of the gauge field, to obtain corrections to the actions for the lower-dimensional Dp-branes. These corrections involve the second fundamental form and correspond to a non-geodesic embedding of the Dp-brane into (flat) ten-dimensional space. In addition, we study the transformation of the corrections under the Seiberg-Witten map relating the ordinary and non-commutative theories. A speculative discussion about the higher-order terms in the derivative expan…
One of explanations of the black hole entropy implies that gravity is entirely induced by quantum effects. By using arguments based on the AdS/CFT correspondence we give induced gravity interpretation of the gravity in a brane world in higher dimensional anti-de Sitter (AdS) space. The underlying quantum theory is SU(N) theory where $N$ is related to the CFT central charge. The theory includes massless fields which correspond to degrees of freedom of the boundary CFT. In addition, on the brane there are massive degrees of freedom with masses proportional to $l^{-1}$ where $l$ is the radius of …
We show how the superembedding formalism can be applied to construct manifestly kappa-symmetric higher derivative corrections for the D9-brane. We also show that all correction terms appear at even powers of the fundamental length scale $l$. We explicitly construct the first potential correction, which corresponds to the kappa-symmetric version of the $\partial^4 F^4$, which one finds from the four-point amplitude of the open superstring.
We disclose the deep connection between the thermodynamics and gravity in a general braneworld model with curvature correction terms on the brane and in the bulk, respectively. We show that the Friedmann equations on the 3-brane embedded in the 5D spacetime with curvature correction terms can be written directly in the form of the first law of thermodynamics on the apparent horizon. Using the first law, we extract the entropy expression of the apparent horizon on the brane, which is useful in studying the thermodynamical properties of the black hole horizon on the brane in Gauss-Bonnet gravity…
General spinning brane bound states are constructed, along with their near-horizon limits which are relevant as dual descriptions of non-commutative field theories. For the spinning D-brane world volume theories with a B-field a general analysis of the gauge coupling phase structure is given, exhibiting various novel features, already at the level of zero angular momenta. We show that the thermodynamics is equivalent to the commutative case at large N and we discuss the possibility and consequences of finite N. As an application of the general analysis, the range of validity of the thermodynam…
In this article we study correspondence between the microscopic spectrum and macroscopic properties of a class of extremal and non-extremal black branes and outline an origin of the interactions among various microstates of a given black brane configuration from the perspective of an intrinsic Riemannian geometry arising from the coarse graining entropy over a large number of microstates. We have analyzed the state-space geometry in the case of various extremal and non-extremal black branes arising from the string theories, multi-centered black brane configurations, small black holes with frac…
The phase diagram for Dp-branes in M-theory compactified on $T^4$, $T^4/Z_2$, $T^5$, and $T^6$ is constructed. As for the lower-dimensional tori considered in our previous work (hep-th/9810224), the black brane phase at high entropy connects onto matrix theory at low entropy; we thus recover all known instances of matrix theory as consequences of the Maldacena conjecture. The difficulties that arise for $T^6$ are reviewed. We also analyze the D1-D5 system on $T^5$; we exhibit its relation to matrix models of M5-branes, and use spectral flow as a tool to investigate the dependence of the phase …
We study the microcanonical description of string gases in the presence of D-branes. We obtain exact expressions for the single string density of states and draw the regions in phase space where asymptotic approximations are valid. We are able to describe the whole range of energies including the SYM phase of the D-branes and we remark the importance of the infrared cut-off used in the high energy approximations. With the complete expression we can obtain the density of states of the multiple string gas and study its thermal properties, showing that the Hagedorn temperature is maximum for ever…
We study the physical process version and the equilibrium state version of the first law of thermodynamics for a charged p-brane. the general setting for our investigations is (n+p+1)-dimensional Einstein dilaton gravity with (p+2) strength form fields.
We study holographic probes dual to heavy quark impurities interpolating between fundamental and symmetric/antisymmetric tensor representations in strongly coupled N=4 supersymmetric gauge theory. These correspond to non-conformal D3- and D5-brane probe embeddings in AdS_5 x S^5 exhibiting flows on their world-volumes. By examining the asymptotic regimes of the embeddings and the one-point function of static fields sourced by the boundary impurity, we conclude that the D5-brane embedding describes the screening of fundamental quarks in the UV into an antisymmetric source in the IR, whilst the …
We present the results of work in which we derived the order rho^2 corrections to the Friedmann equations in the Randall-Sundrum I model. The effects of Golberger-Wise stabilization are taken into account. We surprisingly find that in the cases of inflation and radiation domination, the leading corrections on a given brane come exclusively from the effects of energy density located on the opposite brane.
A vacuum solution of anomaly-free N=1, D=10 Dual Supergravity is constructed. This vacuum corresponds to the presence of two 5-branes, intersecting along M_4, and possesses N=1, D=4 supersymmetry.
A collapsing spherical D2-brane carrying magnetic flux can be described in the region of small radius in a dual zero-brane picture using Tseytlin's proposal for a non-Abelian Dirac-Born-Infeld action for N D0-branes. A standard large N approximation of the D0-brane action, familiar from the brane dielectric effect, gives a time evolution which agrees with the Abelian D2-brane Born-Infeld equations which describe a D2-brane collapsing to zero size. The first 1/N correction from the symmetrised trace prescription in the zero-brane action leads to a class of classical solutions where the minimum …
We discuss quantum corrections to extremal black brane solutions in N=2 U(1) gauged supergravity in four dimensions. We consider modifications due to a certain class of higher-derivative terms as well as perturbative corrections to the prepotential. We use the entropy function formalism to assess the impact of these corrections on singular brane solutions and we give a few examples. We then use first-order flow equations to construct solutions that interpolate between quantum corrected fixed points of the associated potentials.
By explicit calculation, we show that the expansion of the disk level S-matrix element of one RR field, two open string tachyons and one gauge field that has been recently found corresponds to the derivative expansion of the Wess-Zumino action of D-brane-anti-D-brane systems.
We consider certain supersymmetric Born-Infeld couplings to the D3 brane action and show that they give rise to massless and massive KK excitations of type IIB on $AdS_5\times S_5$, in terms of singleton Yang-Mills superfields.
Motivated by a recent work on asymptotically AdS_4 black holes in M-theory, we investigate the thermodynamics and thermodynamical geometry of AdS black holes from M2 and M5-branes. Concretely, we consider AdS black holes in AdS_{p+2}\times S^{11-p-2}, where p=2,5 by interpreting the number of M2 (and M5-branes) as a thermodynamical variable. We study the corresponding phase transition to examine their stabilities by calculating and discussing various thermodynamical quantities including the chemical potential. Then, we compute the thermodynamical curvatures from the Quevedo metric for M2 and M…
We calculate the string loop corrections to the tachyon potential for stable non-BPS Dp-branes on the orbifold T^4/Z_2. We find a non-trivial phase structure and we show that, after tachyon condensation, the non-BPS Dp-branes are attracted to each other for p=0,1,2. We then identify the corresponding closed string boundary states together with the massless long range fields they excite. For p=3,4 the string loop correction diverge. We identify the massless closed string fields responsible for these divergencies and regularise the partition function using a Fischler-Susskind mechanism.
We continue with the analysis of finite temperature corrections to the Tachyon mass in intersecting branes which was initiated in arxiv:1403.0389. In this paper we extend the computation to the case of intersecting D3-branes by considering a setup of two intersecting branes in flat-space background. A holographic model dual to BCS superconductor consisting of intersecting D8-branes in D4-brane background was proposed in arxiv:1104.2843. The background considered here is a simplified configuration of this dual model. We compute the one-loop Tachyon amplitude in the Yang-Mills approximation and …
The universal thermodynamic relations between corrections to entropy and extremality for various black holes solutions have been studied. In this regard, we hereby consider a number of different black brane solutions in different structures for perturbative corrections to general relativity. These are, namely, black brane solution in Rastall AdS massive gravity, Einstein-Yang-Mills AdS black brane solution in massive gravity and general anisotropic black brane in Horava-Lifshitz gravity. We calculate both the entropy and extremality bound by introducing a small constant correction to the actio…
We study the holographic dual of flavors in a Chern-Simons matter theory at non-zero temperature, realized as D6-branes in the type IIA black hole dual in the ABJM background geometry. We consider both massive and massless flavors. The former are treated in the quenched approximation, whereas the massless ones are considered as dynamical objects and their backreaction on the geometry is included in the black hole background. We compute the holographically renormalized action of the probe by imposing several physical conditions. In the limit of massless flavors the free energy and entropy of th…
Black p-brane Thermodynamics without Constructing Solutions
Center for Joint Quantum Studies, Department of Physics, School of Science, Tianjin University（天津大学理学院物理系联合量子研究中心）；The International Joint Institute of Tianjin University, Fuzhou, Tianjin University（天津大学福州国际联合学院）
