We study the partition functions of BPS vortices and magnetic monopole operators, in gauge theories describing $N$ M2-branes. In particular, we explore two closely related methods to study the Cardy limit of the index on $S^2\times\mathbb{R}$. The first method uses the factorization of this index to vortex partition functions, while the second one uses a continuum approximation for the monopole charge sums. Monopole condensation confines most of the $N^2$ degrees of freedom except $N^{\frac{3}{2}}$ of them, even in the high temperature deconfined phase. The resulting large $N$ free energy statistically accounts for the Bekenstein-Hawking entropy of large BPS black holes in $AdS_4\times S^7$. Our Cardy free energy also suggests a finite $N$ version of the $N^{\frac{3}{2}}$ degrees of freedom.
We construct the effective theory of intersecting branes and investigate the BPS monopoles in the theory. The monopoles obtained are the generalization of Nielsen-Olesen vortex. We study the properties of the solutions and interpret them as the D0-branes on the brane-intersections.
We investigate an action which resembles the effective action of brane-antibrane system derived from boundary string field theory. We find that the action has smooth vortex solutions which saturate the Bogomol'nyi bound.
The point where a D2-brane intersecting a stack of D2-branes is proposed as a candidate for the 't Hooft vortex in the world-volume theory of N D2-branes. This straightforwardly generalizes to D3-branes, where a vortex line is generated by the intersection. Similarly, there are such objects on M-branes. We use Maldacena's conjecture to compute the static potential between a vortex and an anti-vortex in each case, in the large N limit.
We propose a novel and simple method to compute the partition function of statistical mechanics of local and semi-local BPS vortices in the Abelian-Higgs model and its non-Abelian extension on a torus. We use a D-brane realization of the vortices and T-duality relation to domain walls. We there use a special limit where domain walls reduce to gas of hard (soft) one-dimensional rods for Abelian (non-Abelian) cases. In the simpler cases of the Abelian-Higgs model on a torus, our results agree with exact results which are geometrically derived by an explicit integration over the moduli space of v…
We investigate a system of 1,3, and 7-branes in type IIB string theory. We identify the 1-brane with the vortex of the Abelian Higgs model. We claim that in the S-dual, the theory on the 3-brane confines electric flux which we identify with the fundamental string and that the dual photon has a mass. We then investigate ways of breaking supersymmetry in the brane set up.
The purpose of this paper is to describe a relationship between the moduli space of vortices and the moduli space of instantons. We study charge k vortices in U(N) Yang-Mills-Higgs theories and show that the moduli space is isomorphic to a special Lagrangian submanifold of the moduli space of k instantons in non-commutative U(N) Yang-Mills theories. This submanifold is the fixed point set of a U(1) action on the instanton moduli space which rotates the instantons in a plane. To derive this relationship, we present a D-brane construction in which the dynamics of vortices is described by the Hig…
We study BPS vortices in the mass-deformed non-relativistic ${\C N}=6$ $U(N)_k\times U(N)_{-k}$ Chern-Simons-matter theory. We focus on the massive deformation that preserves the maximal ${\C N}=6$ supersymmetry, and consider a non-relativistic limit that carry 14 supercharges. In this non-relativistic field theory we find Jackiw-Pi type exact vortex solutions combined with $S^3$ fuzzy sphere geometry. We analyse their properties and show that they preserve one dynamical, one conformal and five kinematical supersymmetries among the full super Schrödinger symmetry.
We study BPS solitons in N=6 U(N) \times U(N) Chern-Simons-matter theory deformed by an F-term mass. The F-term mass generically breaks N=6 supersymmetry down to N=2. At vacua, M2-branes are polarized into a fuzzy S^3 forming a spherical M5-brane with topology \mathbf{R}^{1,2} \times S^3. The polarization is interpreted as Myers' dielectric effect caused by an anti-self-dual 4-form flux T_4 in the eleven-dimensional supergravity. Assuming a polarized M2-brane configuration, the model effectively reduces to the well-known abelian Chern-Simons-Higgs model studied in detail by Jackiw-Lee-Weinberg…
A Nielsen-Olesen vortex usually sits in an environment that expels the flux that is confined to the vortex, so flux is not present both inside and outside. We construct vortices for which this is not true, where the flux carried by the vortex also permeates the `bulk' far from the vortex. The idea is to mix the vortex's internal gauge flux with an external flux using off-diagonal kinetic mixing. Such `dark' vortices could play a phenomenological role in models with both cosmic strings and a dark gauge sector. When coupled to gravity they also provide explicit ultra-violet completions for codim…
In the Seiberg-Witten limit, the low-energy dynamics of N weakly coupled identical open strings on a D3-brane can behave as two-dimensional incompressible hydrodynamics. Classical vortices are frozen in the fluid and described by an action expressed in terms of two canonical conjugate fields, which can be taken as the new space coordinate. The noncommutative space naturally arises when this pair of conjugate fields are quantized. To the lowest order of $\hbar$, the vorticity can replace the background $B$-field on the D3 brane, thereby yielding a spatially and temporally varying noncommutative…
We study the moduli spaces of k U(N) vortices which are realized by the Higgs branch of a U(k) supersymmetric gauge theory. The theory has 4 supercharges and lives on k D1-branes in a N D3- and NS5-brane background. We realize the vortex moduli space as a C* projection of the vortex master space. The Hilbert series is calculated in order to characterize the algebraic structure of the vortex master space and to identify the precise C* projection. As a result, we are able to fully classify the moduli spaces up to 3 vortices.
We construct explicit BPS and non-BPS solutions of the Yang-Mills equations on the noncommutative space R^{2n}_θx S^2 which have manifest spherical symmetry. Using SU(2)-equivariant dimensional reduction techniques, we show that the solutions imply an equivalence between instantons on R^{2n}_θx S^2 and nonabelian vortices on R^{2n}_θ, which can be interpreted as a blowing-up of a chain of D0-branes on R^{2n}_θinto a chain of spherical D2-branes on R^{2n} x S^2. The low-energy dynamics of these configurations is described by a quiver gauge theory which can be formulated in terms of new geometri…
Non-abelian gauge theories in the Higgs phase admit a startling variety of BPS solitons. These include domain walls, vortex strings, confined monopoles threaded on vortex strings, vortex strings ending on domain walls, monopoles threaded on strings ending on domain walls, and more. After presenting a self-contained review of these objects, including several new results on the dynamics of domain walls, we go on to examine the possible interactions of solitons of various types. We point out the existence of a classical binding energy when the string ends on the domain wall which can be thought o…
We study the behaviour of Polyakov confining string in the Georgi-Glashow model in three dimensions near confining-deconfining phase transition described in hep-th/0010201. In the string language, the transition mechanism is the decay of the confining string into D0 branes (charged W bosons of the Georgi-Glashow model). In the world-sheet picture the world-lines of heavy D0 branes at finite temperature are represented as world-sheet vortices of a certain type, and the transition corresponds to the condensation of these vortices. We also show that the ``would be'' Hagedorn transition in the con…
We consider equivariant dimensional reduction of Yang-Mills theory on K"ahler manifolds of the form M times CP^1 times CP^1. This induces a rank two quiver gauge theory on M which can be formulated as a Yang-Mills theory of graded connections on M. The reduction of the Yang-Mills equations on M times CP^1 times CP^1 induces quiver gauge theory equations on M and quiver vortex equations in the BPS sector. When M is the noncommutative space R_theta^{2n} both BPS and non-BPS solutions are obtained, and interpreted as states of D-branes. Using the graded connection formalism, we assign D0-brane ch…
We construct explicit BPS and non-BPS solutions of the U(2k) Yang-Mills equations on the noncommutative space R^{2n}_θx S^2 with finite energy and topological charge. By twisting with a Dirac multi-monopole bundle over S^2, we reduce the Donaldson-Uhlenbeck-Yau equations on R^{2n}_θx S^2 to vortex-type equations for a pair of U(k) gauge fields and a bi-fundamental scalar field on R^{2n}_θ. In the SO(3)-invariant case the vortices on R^{2n}_θdetermine multi-instantons on R^{2n}_θx S^2. We show that these solutions give natural physical realizations of Bott periodicity and vector bundle modifica…
We study analytically and numerically the core structure of global vortices forming on topologically deformed brane-worlds with a single toroidally compact extra dimension. It is shown that for an extra dimension size larger than the scale of symmetry breaking the magnitude of the complex scalar field at the vortex center can dynamically remain non-zero. Singlevaluedness and regularity are not violated. Instead, the winding escapes to the extra dimension at the vortex center. As the extra dimension size decreases the field magnitude at the core dynamically decreases also and in the limit of ze…
We construct Nielsen-Olesen vortex solution in the noncommutative abelian Higgs model. We derive the quantized topological flux of the vortex solution. We find that the flux is integral by explicit computation in the large $θ$ limit as well as in the small $θ$ limit. In the context of a tachyon vortex on the brane-antibrane system we demonstrate that it is this topological charge that gives rise to the RR charge of the resulting BPS D-brane. We also consider the left-right-symmetric gauge theory which does not have a commutative limit and construct an exact vortex solution in it.
Recently, some authors have considered the quantum spectrum of black holes . This consideration is extended to tachyonic black holes in a brane-anti-brane system. In this study, black holes are constructed from two branes which are connected by a tachyonic tube. As the branes come closer to each other, they evolve and make a transition to thermal black branes. It will be shown that the spectrum of these black holes depends on the tachonic potential and the separation distance between the branes. By decreasing the separation distance, more energy emerges and the spectrum of the black hole incre…
We develop the quasi-particle picture for Schwarzchild and far from extremal black holes. We show that the thermalization equations of the black hole is recovered from the model of branes and anti-branes. This can also be viewed as a field theory explanation of the relationship between area and entropy for these black holes. As a by product the annihilation rate of branes and anti-branes is computed.
The worldvolume field equations of M-branes and D-branes are known to admit p-brane soliton solutions. These solitons are shown to saturate a BPS-type bound on their p-volume tensions, which are expressed in terms of central charges that are expected to appear in the worldvolume supertranslation algebra. The cases we consider include vortices, `BIons', instantons and dyons (both abelian and non-abelian), and the string boundaries of M-2-branes in the M-5-brane.
We calculate the potential between two different stationary D-branes and the velocity dependent potential between two different moving D-branes. We identify configurations with some unbroken supersymmetry, using a zero force condition. The potentials are compared with an eleven dimensional calculation of the scattering of a zero black-brane from the $0,2,4$ and 6 black-brane of type IIA supergravity. The agreement of these calculations provide further evidence for the D-brane description of black-branes, and for the eleven dimensional origin of type IIA string theory.
We construct explicit BPS and non-BPS solutions of the Yang-Mills equations on noncommutative spaces R^{2n}_theta x G/H which are manifestly G-symmetric. Given a G-representation, by twisting with a particular bundle over G/H, we obtain a G-equivariant U(k) bundle with a G-equivariant connection over R^{2n}_theta x G/H. The U(k) Donaldson-Uhlenbeck-Yau equations on these spaces reduce to vortex-type equations in a particular quiver gauge theory on R^{2n}_theta. Seiberg-Witten monopole equations are particular examples. The noncommutative BPS configurations are formulated with partial isometrie…
Using a reformulation of topological ${\cal N}=2$ QFT's in M-theory setup, where QFT is realized via M5 branes wrapping co-associative cycles in a $G_2$ manifold constructed from the space of self-dual 2-forms over $X^4$, we show that superconducting vortices are mapped to M2 branes stretched between M5 branes. This setup provides a physical explanation of Taubes' construction of the Seiberg-Witten invariants when $X^4$ is symplectic and the superconducting vortices are realized as pseudo-holomorphic curves. This setup is general enough to realize topological QFT's arising from ${\cal N}=2$ QF…
We consider configurations of D6-branes with D0-brane charge given by recent work of Taylor and compute interaction potentials with various D-brane probes using a 1-loop open string calculation. These results are compared to a supergravity calculation using the solution given by Sheinblatt of an extremal black hole carrying 0-brane and 6-brane charge.
Five dimensional neutral rotating black rings are described from a Randall-Sundrum brane world perspective in the bulk black string framework. To this end we consider a rotating black string extension of a five dimensional black ring into the bulk of a six dimensional Randall-Sundrum brane world with a single four brane. The bulk solution intercepts the four brane in a five dimensional black ring with the usual curvature singularity on the brane. The bulk geodesics restricted to the plane of rotation of the black ring are constructed and their projections on the four brane match with the usual…
We explore the problem of braneworld black holes in the heterotic braneworld scenario of Lukas, Ovrut, Stelle and Waldram (LOSW). We show that black string solutions are unstable, and demonstrate some unusual asymptotics in the linearized metric. We also solve the fully coupled brane and bulk Einstein equations, finding an exact, though singular, solution which corresponds to a brane black hole in which the branes spike apart at the Schwarzschild radius.
We generalise all the known supersymmetric composite M-branes to the corresponding black configurations. Thermodynamical formulae is written by using the simple rules to construct these black branes.
We consider D-brane/anti-D-brane systems at T>0. Starting at the closed string vacuum, we argue that a finite temperature leads to the reappearance of open string degrees of freedom. We also show that, at a sufficiently large temperature, the open string vacuum becomes stable. Building upon this observation and previous work by Horowitz, Maldacena and Strominger, we formulate a microscopic brane-antibrane model for the non-extremal black three-brane in ten dimensions (as well as for the black two- and five-branes in eleven dimensions). Under reasonable assumptions, and using known results from…
We find half-BPS vortex solitons, at both weak and strong coupling, in the N=6 supersymmetric mass deformation of ABJM theory with U(N) x U(N) gauge symmetry and Chern-Simons level k. The strong coupling gravity dual is obtained by performing a Z_k quotient of the N=8 supersymmetric eleven dimensional supergravity background of Lin, Lunin and Maldacena corresponding to the mass deformed M2-brane theory. At weak coupling, the BPS vortices preserving six supersymmetries are found in the Higgs vacuum of the theory where the gauge symmetry is broken to U(1) x U(1). The classical vortex solitons br…
A five dimensional rotating black string in a Randall-Sundrum brane world is considered. The black string intercepts the three brane in a four dimensional rotating black hole. The geodesic equations and the asymptotics in this background are discussed.
We prove the uniqueness of higher dimensional (dilatonic) charged black holes in static and asymptotically flat spacetimes for arbitrary vector-dilaton coupling constant. An application to the uniqueness of a wide class of black p-branes is also given.
We study stationary black brane solutions in the context of N = 2, U(1) gauged supergravity in five dimensions. Using the formalism of first-order flow equations, we construct examples of extremal black brane solutions that include Nernst branes, i.e. extremal black brane solutions with vanishing entropy density, as well as black branes with cylindrical horizon topology, whose entropy density can be computed from a Cardy formula of the dual CFT.
We continue consideration of models where the Higgs effect is produced by the presence of 3-brane fluctuating in compact extra dimensions. The consistent examples of such models may be obtained from previously known solutions of 6D supergravity. The low-energy limit for these models coincides with a version of Higgs model written in terms of gauge-invariant supercurrent variables. We also elaborate on vortices in the Abelian version of the theory and show how vortices that are singular from the 4D point of view become allowed due to higher-dimensional resolution of singularity.
We argue the existence of solutions of the Euclidean Einstein equations that correspond to a vortex sitting at the horizon of a black hole. We find the asymptotic behaviours, at the horizon and at infinity, of vortex solutions for the gauge and scalar fields in an abelian Higgs model on a Euclidean Schwarzschild background and interpolate between them by integrating the equations numerically. Calculating the backreaction shows that the effect of the vortex is to cut a slice out of the Euclidean Schwarzschild geometry. Consequences of these solutions for black hole thermodynamics are discussed.
We construct in the supergravity framework a relation between thermal chargeless non-extremal black three-branes and thermal Dirichlet branes-antibranes systems. We propose this relation as a possible explanation for the intriguing similarity between the black branes Bekenstein-Hawking entropy and the field theory entropy of thermal branes-antibranes. We comment on various relations between branes, antibranes and non-BPS branes in type II string theories.
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 thermodynami…
A general black-branes system under the T-duality transformation will become another smeared system with different dimensional black branes. We first use some simple examples to see that both systems have a same value of entropy and then present a rigorous method to prove this general property. Using the property we could easily know the entropy of some complex black-brane systems.
We study the process of black brane evaporation through the emission of D-branes. Gravitational solutions describing black branes in asymptotically anti-de Sitter spacetimes, which are holographically dual to field theory states at finite temperature and density, have previously been found to exhibit an instability due to brane nucleation. Working in the setting of D3-branes on the conifold, we construct static Euclidean solutions describing this nucleation to leading order - D3-branes bubbling off the horizon. Furthermore, we analyze the late-time dynamics of such a D3-brane bubble as it expa…
A black string generaliztion of the Myers-Perry N dimensional rotating black hole is considered in an (N+1) dimensional Randall-Sundrum brane world. The black string intercepts the (N-1) brane in a N dimensional rotating black hole. We examine the diverse cases arising for various non-zero rotation components and obtain the geodesic equations for these space-time. The asymptotics of theresulting brane world geometries and their implications are discussed.
We present non-extreme generalisations of intersecting p-brane solutions of eleven-dimensional supergravity which upon toroidal compactification reduce to non-extreme static black holes in dimensions D=4, D=5 and 5<D<10, parameterized by four, three and two charges, respectively. The D=4 black holes are obtained either from non-extreme configuration of three intersecting five-branes with a boost along the common string or from non-extreme intersecting system of two two-branes and two five-branes. The D=5 black holes arise from three intersecting two-branes or from a system of intersecting two-…
In this paper, we use only the equation of motion for an interacting system of gravity, dilaton and antisymmetric tensor to study the black brane solutions. By making use of the property of Schwarzian derivative, we obtain the complete solution of this system of equations. For some special values we obtain the well-known BPS brane and black brane solutions.
In this note we study bulk timelike geodesics in the presence of a brane-world black hole, where the brane-world is a two-brane moving in a 3+1-dimensional asymptotically $adS_4$ spacetime. We show that for a certain range of the parameters measuring the black hole mass and bulk cosmological constant, there exist stable timelike geodesics which orbit the black hole and remain bound close to the two-brane.
There exists a dramatic difference in phase structure between charged black Dp-branes with $p < 5$ and charged black D5 or D6 branes. In [1], we found that the phase structure of charged black D5 system can be changed qualitatively to that of charged black Dp with $p < 5$ by adding the delocalized D1 branes but the similar change does not happen for the charged black D6 system through adding the delocalized D2 branes (Note that both D1/D5 and D2/D6 belong to the same type of D(p - 4)/Dp system). Adding the delocalized D4 branes to the black D6 branes doesn't work, either. In this paper, we con…
In this paper, which is a companion to ArXiv:1204.2711[hep-th], we formulate a criterion for constructing 11D/10D maximal supergravity black-brane solutions with the near-extremal $S\sim n^3T^5$ entropy-temperature relation. We present explicit examples of such solutions with special attention paid to thermodynamics of black M-waves (KK-waves), intersecting/interpolating black branes with KK-waves, M2/M5 branes and their descents. We find the conditions on charges and numbers of branes in intersections, under which the dielectric effect of brane polarization becomes manifest on the supergravit…
Thermodynamics of the near extremal black p-branes can be described by collective motions of gravitationally interacting branes. This proposal is called the p-soup model. In this paper, we check this proposal in the case of black brane system which is asymptotically Friedmann-Lemaitre-Robertson-Walker universe in an infinite distance. As a result, we can show that the gravitationally interacting branes explain free energy, entropy, temperature and other physical quantities in these systems. This implies that the microstates of this kind of brane system can be also understood in the p-soup mode…
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.
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 entropy of a near-extremal black hole made of parallel D-branes has been shown to agree, upto a numerical factor, with that of the gas of massless open string states on the brane worldvolume when the string coupling is chosen suitably. We investigate the process of emission or absorption of massless S-wave neutral scalars by these black holes. We show that with rather mild assumptions about the nature of the interactions between the scalar and open string states, the D-brane cross-section generally fails to reproduce the universal low energy black hole cross-section except for 1-branes and…
We find the probe D5-brane solution on the black home spacetime which is asymptomatically AdS_5 x S^5. These black holes have spherical, hyperbolic and toroidal structures. Depending on the gauge flux on the D5-brane, the D5-brane behaves differently. This By adding the fundamental string, the potential energy of the interface solution and the Wilson loop is given in the case of non zero gauge flux.
In this paper we discuss the M-brane description for a N=2 black hole. This solution is a result of the compactification of M-5-brane configurations over a Calabi-Yau threefold with arbitrary intersection numbers $C_{ABC}$. In analogy to the D-brane description where one counts open string states we count here open 2-branes which end on the M-5-brane.
Codimension-two objects on a system of brane-antibrane are studied in the context of Born-Infeld type effective field theory with a complex tachyon and U(1)$\times$U(1) gauge fields. When the radial electric field is turned on in D2${\bar {\rm D}}$2, we find static regular global and local D-vortex solutions which could be candidates of straight cosmic D-strings in a superstring theory. A natural extension to DF-strings is briefly discussed.
We study a class of topological black hole solutions in RSII braneworld scenario in the presence of a localized Maxwell field on the brane. Such a black hole can carry two types of charge, one arising from the extra dimension, the tidal charge, and the other one from a localized gauge field confined to the brane. We find that the localized charge on the brane modifies the bulk geometry and in particular the bulk Weyl tensor. The bulk geometry does not depend on different topologies of the horizons. We present the temperature and entropy expressions associated with the event horizon of the bran…
We study static brane configurations in the bulk background of the topological black holes in asymptotically flat spacetime. We find that such configurations are possible even for flat black hole horizon, unlike the AdS black hole case. We construct the brane world model with an orbifold structure S^1/Z_2 in such bulk background. We also study massless bulk scalar field.
We consider a one-brane probe in the presence of a five-dimensional black hole in the classical limit. The velocity-dependent force on a slowly-moving probe is characterized by a metric on the probe moduli space. This metric is computed for large black holes using low-energy supergravity, and for small black holes using D-brane gauge theory. The results are compared.
I show how the AdS2 D-branes in the Euclidean AdS3 string theory are related to the continuous D-branes in Liouville theory. I then propose new discrete D-branes in the Euclidean AdS3 which correspond to the discrete D-branes in Liouville theory. These new D-branes satisfy the appropriate shift equations. They give rise to two families of discrete D-branes in the 2d black hole, which preserve different symmetries.
D-branes have been used to describe many properties of extremal and near extremal black holes. These lecture notes provide a short review of these developments.
We discuss black hole solutions with a Gauss-Bonnet term in the bulk and an induced gravity term on a thin brane of codimension-2. We show that these black holes can be localized on the brane, and they can be extended further into the bulk by a warp function. These solutions have regular horizons and no other curvature singularities appear apart from the string-like ones. The projection of the Gauss-Bonnet term on the brane imposes a constraint relation which dictates the form of matter on the brane and in the bulk.
