Dimensional Worldvolume Research Articles

Phase diagram of QCD matter with magnetic field: domain-wall Skyrmion chain in chiral soliton lattice

QCD matter in strong magnetic field exhibits a rich phase structure. In the presence of an external magnetic field, the chiral Lagrangian for two flavors is accompanied by the Wess-Zumino-Witten (WZW) term containing an anomalous coupling of the neutral pion π0 to the magnetic field via the chiral anomaly. Due to this term, the ground state is inhomogeneous in the form of either chiral soliton lattice (CSL), an array of solitons in the direction of magnetic field, or domain-wall Skyrmion (DWSk) phase in which Skyrmions supported by π3[SU(2)] ≃ ℤ appear inside the solitons as topological lumps supported by π2(S2) ≃ ℤ in the effective worldvolume theory of the soliton. In this paper, we determine the phase boundary between the CSL and DWSk phases beyond the single-soliton approximation, within the leading order of chiral perturbation theory. To this end, we explore a domain-wall Skyrmion chain in multiple soliton configurations. First, we construct the effective theory of the CSL by the moduli approximation, and obtain the ℂP1 model or O(3) model, gauged by a background electromagnetic gauge field, with two kinds of topological terms coming from the WZW term: one is the topological lump charge in 2+1 dimensional worldvolume and the other is a topological term counting the soliton number. Topological lumps in the 2+1 dimensional worldvolume theory are superconducting rings and their sizes are constrained by the flux quantization condition. The negative energy condition of the lumps yields the phase boundary between the CSL and DWSk phases. We find that a large region inside the CSL is occupied by the DWSk phase, and that the CSL remains metastable in the DWSk phase in the vicinity of the phase boundary.

Cosmologies inside hyperbolic black holes

Models with closed FRW cosmologies on the worldvolume of a constant-tension brane inside a black hole provide an interesting setup for studying cosmology holographically. However, in more than two worldvolume dimensions, there are limitations on such models with flat spatial slices. I show that these limitations can be avoided by considering instead hyperbolic slices. This also naturally makes contact with previous work on Euclidean wormholes.

The FGK formalism for black p-branes in d dimensions

We present a generalization to an arbitrary number of spacetime (d) and worldvolume (p+1) dimensions of the formalism proposed by Ferrara, Gibbons and Kallosh to study black holes (p=0) in d=4 dimensions. We include the special cases in which there can be dyonic and self- or anti-self-dual black branes. Most of the results valid for 4-dimensional black holes (relations between temperature, entropy and non-extremality parameter, and between entropy and black-hole potential on the horizon) are straightforwardly generalized. We apply the formalism to the case of black strings in N=2,d=5 supergravity coupled to vector multiplets, in which the black-string potential can be expressed in terms of the dual central charge and work out an explicit example with one vector multiplet, determining supersymmetric and non-supersymmetric attractors and constructing the non-extremal black-string solutions that interpolate between them.

ON p-BRANES AND ANTISYMMETRIC NON-ABELIAN TENSORIAL GAUGE FIELD THEORIES OF DIFFEOMORPHISMS

It is shown how actions corresponding to antisymmetric non-Abelian tensorial gauge field theories of (p+1)-dimensional diffeomorphisms yield p-brane actions associated with their (p+1)-dimensional worldvolume evolution. We conclude with a discussion of how to obtain p-brane actions from the large N limit of covariant matrix models based on generalized hypermatrices. A deformation quantization of Nambu classical mechanics furnishing Nambu quantum mechanics by constructing the n-ary noncommutative product of n functions f1 •f2 • ⋯ •fn, the n-ary version of the Moyal bracket, and the analog of the Weyl–Wigner–Groenowold–Moyal map among operators and c-functions remains an open problem. A solution to this problem will reveal important relations between the physics of p-branes and matrix models based on generalized hypermatrices in the large N limit.

“Mass inflation” with lightlike branes

Abstract We discuss properties of a new class of p-brane models, describing intrinsically lightlike branes for any world-volume dimension, in various gravitational backgrounds of interest in the context of black hole physics. One of the characteristic features of these lightlike p-branes is that the brane tension appears as an additional nontrivial dynamical world-volume degree of freedom. Codimension one lightlike brane dynamics requires that bulk space with a bulk metric of spherically symmetric type must possess an event horizon which is automatically occupied by the lightlike brane while its tension evolves exponentially with time. The latter phenomenon is an analog of the well known “mass inflation” effect in black holes.

Weyl-conformally-invariant lightlikep-brane theories: New aspects in black hole physics and Kaluza-Klein dynamics

We introduce and study in some detail the properties of a novel class of Weyl-conformally invariant p-brane theories which describe intrinsically lightlike branes for any odd world-volume dimension. Their dynamics significantly differs from that of the ordinary (conformally non-invariant) Nambu-Goto p-branes. We present explicit solutions of the Weyl-invariant lightlike brane- (WILL-brane) equations of motion in various gravitational models of physical relevance exhibiting various new phenomena. In D=4 the WILL-membrane serves as a material and charged source for gravity and electromagnetism in the coupled Einstein-Maxwell-WILL-membrane system; it automatically positions itself on (``straddles'') the common event horizon of the corresponding matching black hole solutions, thus providing an explicit dynamical realization of the membrane paradigm in black hole physics. In product spaces of interest in Kaluza-Klein theories the WILL-brane wraps non-trivially around the compact (internal)dimensions and still describes massless mode dynamics in the non-compact (space-time) dimensions. Due to nontrivial variable size of the internal compact dimensions we find new types of physically interesting solutions describing massless brane modes trapped on bounded planar circular orbits with non-trivial angular momentum, and with linear dependence between energy and angular momentum.

Einstein gravity on an even-codimension brane

We give the equations of motion for a self-gravitating Dirac $p$-brane embedded in an even codimension spacetime. The dynamics of the bulk are dictated by Lovelock gravity and permit matching conditions, even when the codimension is strictly greater than 2. We show that the equations of motion involve both induced Lovelock densities on the brane and regular extrinsic curvature terms. The brane dynamics can be derived from an exact $(p+1)$-dimensional induced action. The Dirac charge is carried by an overall (solid) angle defect which sets the Planck scale on the brane. In particular, if the codimension is greater than the world-volume dimension of the $p$-brane, we show that the extrinsic curvature terms cancel, leaving an exact induced Lovelock theory. For example, a 3-brane embedded in 8 or 10 dimensions obeys Einstein's equations with a cosmological constant.

Charged and uncharged D-branes in various string theories

We describe how the D-brane spectra of the various ten-dimensional string theories can be related to general properties of the open–closed duality, encoded in the S and P matrices of the conformal field theory. We also complete the classification and the description of non-BPS branes in these string theories, elucidating their non-Abelian structures and the nature of the corresponding super-Higgs mechanisms. We find that the type 0 theories and their orientifolds have two types of uncharged branes, distinguished by their couplings to the closed string tachyon. We also find that the 0A orientifold has the unusual feature of having charged and uncharged branes with identical world-volume dimensions. We conclude with some comments on fractional branes, elucidating their role in connection with the boundary states of D odd SU(2) WZW models.

7-branes and higher Kaluza–Klein branes

We present and study a new chain of 10-d T duality related solutions and their 11-d parents whose existence had been predicted in the literature based in U duality requirements in 4 d. The first link is the S dual of the D7-brane. The next link has 6 spatial worldvolume dimensions, it is charged w.r.t. the RR 7-form but depends only on 2 transverse dimensions since the third has to be compactified in a circle and is isometric and hence is similar in this respect to the KK monopole. The next link has 5 spatial worldvolume dimensions, it is charged w.r.t. the RR 6-form but depends only on 2 transverse dimensions since the 3rd and 4th have to be compactified in circles and are isometric and so on. All these solutions are identical when reduced over the p spatial worldvolume dimensions and preserve a 1/2 on the supersymmetries. Their masses depend on the square of the radii of the isometric directions, just as for the KK monopole. We give a general map of these branes and their duality relations and show how they must appear in the supersymmetry algebra.

Space-time-filling branes and strings with sixteen supercharges

We discuss branes whose world-volume dimension equals the target space-time dimension, i.e. “space-time-filling branes”. In addition to the D9-branes, there are 9-branes in the NS–NS sectors of both the IIA and IIB strings. The world-volume actions of these branes are constructed, via duality, from the known actions of branes with codimension larger than zero. Each of these types of branes is used in the construction of a string theory with sixteen supercharges by modding out a Type II string by an appropriate discrete symmetry and adding 32 9-branes. These constructions are related by a web of dualities and each arises as a different limit of the Hořava–Witten construction.

Spacetime-Filling Branes and Strings with Sixteen Supercharges

We discuss branes whose worldvolume dimension equals the target spacetime dimension, i.e. ‘spacetime-filling branes’. In addition to the D9-branes, there are 9-branes in the NS-NS sectors of both the IIA and IIB strings. Each of these types of branes is used in the construction of a string theory with sixteen supercharges by modding out a type II string by an appropriate discrete symmetry and adding 32 9-branes. These constructions are related by a web of dualities and each arises as a different limit of the Hořava-Witten construction.

Brane mapping under (−1) FL

We present the evidence that (−1) F L is a nonperturbative symmetry of Type II string theory. We argue that (−1) F L is a symmetry of string theory as much as the SL(2, Z) of the Type II string is and how the branes are mapped under the (−1) F L modding. NS branes are mapped into the NS branes with the same world volume dimensions but with the different chiral structure. Supersymmetric D p-branes (bound with anti-D p branes) are mapped to unstable nonsupersymmetric D p-branes, which has D( p−1)-branes as kink solutions according to Horava [Type IIA D-branes, K Theory, And Matrix Theory, hep-th/9812135].

Kaluza-Klein states from large extra dimensions

We consider the novel Kaluza-Klein (KK) scenario where gravity propagates in the $4+n$ dimensional bulk of spacetime, while gauge and matter fields are confined to the 3+1 dimensional world-volume of a brane configuration. For simplicity we assume compactification of the extra $n$ dimensions on a torus with a common scale $R$, and identify the massive KK states in the four-dimensional spacetime. For a given KK level $\vec{n}$ there are one spin-2 state, $(n-1)$ spin-1 states and $n(n-1)/2$ spin-0 states, all mass-degenerate. We construct the effective interactions between these KK states and ordinary matter fields (fermions, gauge bosons and scalars). We find that the spin-1 states decouple and that the spin-0 states only couple through the dilaton mode. We then derive the interacting Lagrangian for the KK states and Standard Model fields, and present the complete Feynman rules. We discuss some low energy phenomenology for these new interactions for the case when 1/R is small compared to the electroweak scale, and the ultraviolet cutoff of the effective KK theory is on the order of 1 TeV.

An Sl(2, Z) multiplet of nine-dimensional type II supergravity theories

We show that only by performing generalized dimensional reductions all possible brane configurations are taken into account and one gets the complete lower-dimensional theory. We apply this idea to the reduction of type IIB supergravity in an SL(2, Z)-covariant way and establish T-duality for the type II superstring effective action in the context of generalized dimensional reduction giving the corresponding generalized Buscher's T-duality rules. The full (generalized) dimensional reduction involves all the S-duals of D7-branes: Q7-branes and a sort of composite 7-branes. The three species constitute an SL(2, Z) triplet. Their presence induces the appearance of the triplet of masses of the 9-dimensional theory. The T-duals, including a “KK-8A-brane”, which must have a compact transverse dimension have to be considered in the type IIA side. Compactification of 11-dimensional KK-9M-branes (a.k.a. M9-branes) on the compact transverse dimension give D8-branes while compactification on a world-volume dimension gives KK-8A-branes. The presence of these KK-monopole-type objects breaks translation invariance and two of them given rise to an SL(2, Z)-covariant massive 11-dimensional supergravity whose reduction gives the massive 9-dimensional type II theories.

Brane dynamics from the Born-Infeld action

We use the abelian Born-Infeld action for the world-volume gauge field and transverse displacement scalars to explore new aspects of D-brane structure and dynamics. We study several classic gauge field configurations, including point charges in any world-volume dimension and vortices in two world-volume dimensions, and show that, with an appropriate excitation of the transverse coordinate field, they are BPS-saturated solutions. The Coulomb point charge solutions turn out to represent, with considerable fidelity, fundamental strings attached to the brane (their magnetic counterparts describe D1-branes attached to D3-branes). We also show that the S-matrix for small excitations propagating on the point charge solution is consistent with (and gives further illuminating information about) Polchinski's effective open string boundary condition.

Super Yang-Mills in (11,3) dimensions

A supersymmetric Yang-Mills system in (11, 3) dimensions is constructed with the aid of two mutually orthogonal null vectors which naturally arise in a generalized spacetime superalgebra. An obstacle encountered in an attempt to extend this result to beyond 14 dimensions is described. A null reduction of the (11, 3) model is shown to yield the known super Yang-Mills model in (10, 2) dimensions. An (8, 8) supersymmetric super Yang-Mills system in (3, 3) dimensions is obtained by an ordinary dimensional reduction of the (11, 3) model, and it is suggested there may exist a superbrane with (3, 3) dimensional worldvolume propagating in (11, 3) dimensions.

Gauge-invariant and gauge-fixed D-brane actions

The first part of this paper presents actions for Dirichlet p-branes embedded in a flat tendimensional space-time. The fields of the (p + 1) -dimensional world-volume theories are the I OD space-time coordinates X, a pair of Majorana-Weyl spinors θ 1 and 02, and a U(1) gauge field A μ . The N = 2A or 2B super-Poincaré group in ten dimensions is realized as a global symmetry. In addition the theories have local symmetries consisting of general coordinate invariance of the world-volume, a local fermionic symmetry (called “kappa”), and U(1) gauge invariance. A detailed proof of the kappa symmetry is given that applies to all cases (p = 0, 1, . , 9). The second part of the paper presents gauge-fixed versions of these theories. The fields of the IOD ( p = 9) gauge-fixed theory are a single Majorana-Weyl spinor A and the U(1) gauge field A μ . This theory, whose action turns out to be surprisingly simple, is a supersymmetric extension of 10D Born-Infeld theory. It has two global supersymmetries: one represents an unbroken symmetry, and the second corresponds to a broken symmetry for which A is the Goldstone fermion. The gauge-fixed supersymmetric D-brane theories with p > 9 can be obtained from the 10D one by dimensional reduction.

D-brane actions with local kappa symmetry

We formulate world-volume actions that describe the dynamics of Dirichlet p-branes in a flat 10d background. The fields in these theories consist of the 10d superspace coordinates ( X m , θ) and an abelian world-volume gauge field A μ . The global symmetries are given by the N = 2A or N = 2B super-Poincaré group, according to whether p is even or odd. The local symmetries in the ( p + 1)-dimensional world volume are general coordinate invariance and a fermionic kappa symmetry.

Effective Lagrangian for quantum black holes

We discuss the most general effective Lagrangian obtained from the assumption that the degrees of freedom to be quantized, in a black hole, are on the horizon. The effective Lagrangian depends only on the induced metric and the extrinsic curvature of the (fluctuating) horizon, and the possible operators can be arranged in an expansion in powers of MP1/M, where MP1 is the Planck mass and M the black hole mass. We perform a semiclassical expansion of the action with a formalism which preserves general covariance explicitly. Quantum fluctuations over the classical solutions are described by a single scalar field living in the (2 + 1)-dimensional world-volume swept by the horizon, with a given coupling to the background geometry. We discuss the resulting field theory and we compute the black hole entropy with our formalism.

Superconformal sigma models in higher than two dimensions

Rigidly superconformal sigma models in higher than two dimensions are constructed. These models rely on the existence of conformal Killing spinors on the ( p + 1)-dimensional worldvolume ( p ⩽ 5), and homothetic conformal Killing vectors in the d-dimensional target space. In the bosonic case, substituting into the action a particular form of the target space metric admitting such Killing vectors, we obtain an action with mainfest worldvolume conformal symmetry, which describes the coupling of d − 1 scalars to a conformally flat metric on the worldvolume. We also construct gauged sigma models with worldvolume conformal supersymmetry. The models considered here are generalizations of the singleton actions on S P × S 1, constructed some time ago by Nicolai and these authors.