0-brane Charge Research Articles

Exceptional reductions

Starting from basic identities of the group E8, we perform progressive reductions, namely decompositions with respect to the maximal and symmetric embeddings of E7 × SU(2) and then of E6 × U(1). This procedure provides a systematic approach to the basic identities involving invariant primitive tensor structures of various irreps of finite-dimensional exceptional Lie groups. We derive novel identities for E7 and E6, highlighting the E8 origin of some well-known ones. In order to elucidate the connections of this formalism to four-dimensional Maxwell–Einstein supergravity theories based on symmetric scalar manifolds (and related to irreducible Euclidean Jordan algebras, the unique exception being the triality-symmetric stu model), we then derive a fundamental identity involving the unique rank-4 symmetric invariant tensor of the 0-brane charge symplectic irrep of U-duality groups, with potential applications in the quantization of the charge orbits of supergravity theories, as well as in the study of multi-center black hole solutions therein.

Magnetic charges in the AdS4 superalgebra osp(4|2)

We discuss the issue of how to include magnetic charges in the AdS(4) superalgebra osp(4|2). It is shown that the usual way of introducing a pseudoscalar central charge on the right hand side of the basic anticommutator does not work, because this breaks SO(2,3) covariance. We propose a way out by promoting the magnetic charge to a vector charge, which amounts to enlarge osp(4|2) to the superconformal algebra su(2,2|1). The conditions for 1/4, 1/2 and 3/4 BPS states are then analyzed. These states form the boundary of the convex cone associated with the Jordan algebra of 4x4 complex hermitian matrices. An Inonu-Wigner contraction of the constructed superalgebra yields a known extension of the Poincare' superalgebra containing electric and magnetic 0-brane charges as well as string- and space-filling 3-brane charges. As an example, we show how some supersymmetric AdS(4) black holes fit into the classification scheme of BPS states.

D-brane Wess-Zumino terms and U-duality

We construct gauge-invariant and U-duality covariant expressions for Wess-Zumino terms corresponding to general Dp-branes (for any p<D) in arbitrary 2<D<11 dimensions. A distinguishing feature of these Wess-Zumino terms is that they contain twice as many scalars as the 10-D compactified dimensions, in line with doubled geometry. We find that for D<10 the charges of the higher-dimensional branes can all be expressed as products of the 0-brane charges, which include the D0-brane and the NS-NS 0-brane charges. We give the general expressions for these charges and show how they determine the non-trivial conjugacy class to which some of the higher-dimensional D-branes belong.

Noncritical Superstrings in a Ramond-Ramond Background

We use the recently found matrix description of noncritical superstring theory of Type 0A to compute tachyon scattering amplitudes in a background with a RR flux. We find that after the string coupling is multiplicatively renormalized, the amplitudes in any genus become polynomial in the RR flux. We propose that in the limit where both the string coupling and the RR flux go to infinity, the theory has a weakly-coupled description in terms of another superstring theory with a vanishingly small RR flux. This duality exchanges the inverse string coupling and the 0-brane charge. The dual superstring theory must have a peculiar property that its only field-theoretic degree of freedom is a massless RR scalar.

Probing black holes in nonperturbative gauge theory

We use a 0-brane to probe a ten-dimensional near-extremal black hole with N units of 0-brane charge. We work directly in dual strongly coupled quantum mechanics, using mean-field methods to describe the black hole background nonperturbatively. We obtain the distribution of W boson masses, and find a clear separation between light and heavy degrees of freedom. To localize the probe we introduce a resolving time and integrate out the heavy modes. After a nontrivial change of coordinates, the effective potential for the probe agrees with supergravity expectations. We compute the entropy of the probe, and find that the stretched horizon of the black hole arises dynamically in quantum mechanics, as thermal restoration of unbroken $U(N+1)$ gauge symmetry. Our analysis of quantum mechanics predicts the correct relation between the horizon radius and entropy of a black hole.

Black hole entropy from nonperturbative gauge theory

We present the details of a mean-field approximation scheme for the quantum mechanics of N D0-branes at finite temperature. The approximation can be applied at strong 't Hooft coupling. We find that the resulting entropy is in good agreement with the Bekenstein-Hawking entropy of a ten-dimensional nonextremal black hole with a 0-brane charge. This result is in accord with the duality conjectured by Itzhaki, Maldacena, Sonnenschein and Yankielowicz. We study the spectrum of single-string excitations within quantum mechanics, and find evidence for a clear separation between light and heavy degrees of freedom. We also present a way of identifying the black hole horizon.

BLACK HOLE THERMODYNAMICS FROM CALCULATIONS IN STRONGLY COUPLED GAUGE THEORY

We develop an approximation scheme for the quantum mechanics of N D0-branes at finite temperature in the 't Hooft large-N limit. The entropy of the quantum mechanics calculated using this approximation agrees well with the Bekenstein-Hawking entropy of a ten-dimensional non-extremal black hole with 0-brane charge. This result is in accord with the duality conjectured by Itzhaki, Maldacena, Sonnenschein and Yankielowicz. Our approximation scheme provides a model for the density matrix which describes a black hole in the strongly-coupled quantum mechanics.

Black hole thermodynamics from calculations in strongly coupled gauge theory.

We develop an approximation scheme for the quantum mechanics of N D0-branes at finite temperature in the 't Hooft large- N limit. The entropy of the quantum mechanics calculated using this approximation agrees well with the Bekenstein-Hawking entropy of a ten-dimensional nonextremal black hole with 0-brane charge. This result is in accordance with the duality conjectured by Itzhaki, Maldacena, Sonnenschein, and Yankielowicz [Phys. Rev. D 58, 046004 (1998)]. Our approximation scheme provides a model for the density matrix which describes a black hole in the strongly coupled quantum mechanics.

D-branes and topological field theories

In the presence of a D-brane a string theory develops a new subsector. We show that for curved D-branes the corresponding sector is a (partially twisted) topological field theory. We use this result to compute the degeneracy of 2-branes wrapped around K3 cycles as well as 3-branes wrapped around CY three-fold vanishing 3-cycles. In both cases we find the degeneracy is in accord with expectation. The counting of BPS states of a gas of 0-branes in the presence of a 4-brane in K3 is considered and it is noted that the effective 0-brane charge is shifted by 1, due to a quantum correction. This is in accord with string duality and the fact that the left-moving ground-state energy of the heterotic string starts at −1. We also show that all the three different topological twistings of four-dimensional N = 4 Yang-Mills theory do arise from curved 3-branes embedded in different spaces (Calabi-Yau manifolds and manifolds with exceptional holonomy groups).