Degeneracy of Decadent Dyons

A quarter-BPS dyon in $\mathcal{N}=4$ super Yang-Mills theory is generically `decadent' in that it is stable only in some regions of the moduli space and decays on submanifolds in the moduli space. Using this fact, and from the degeneracy of the system close to the decay, a new derivation for the degeneracy of such dyons is given. The degeneracy obtained from these very simple physical considerations is in precise agreement with the results obtained from index computations in all known cases. Similar considerations apply to dyons in $\mathcal{N}=2$ gauge theories. The relation between the $\mathcal{N} =4$ field theory dyons and those counted by the Igusa cusp form in toroidally compactified heterotic string is elucidated.Comment: Some typos corrected and references adde

Nernst branes in gauged supergravity

We study static black brane solutions in the context of N = 2 U(1) gauged supergravity in four dimensions. Using the formalism of first-order flow equations, we construct novel extremal black brane solutions including examples of Nernst branes, i.e. extremal black brane solutions with vanishing entropy density. We also discuss a class of non-extremal generalizations which is captured by the first-order formalism.Comment: 44 pages, 3 figures, v2: added appendix B and references, minor typographic changes, v3: added some clarifying remarks, version published in JHE

Matrix dynamics of fuzzy spheres

We study the dynamics of fuzzy two-spheres in a matrix model which represents string theory in the presence of RR flux. We analyze the stability of known static solutions of such a theory which contain commuting matrices and SU(2) representations. We find that irreducible as well as reducible representations are stable. Since the latter are of higher energy, this stability poses a puzzle. We resolve this puzzle by noting that reducible representations have marginal directions corresponding to non-spherical deformations. We obtain new static solutions by turning on these marginal deformations. These solutions now have instability or tachyonic directions. We discuss condensation of these tachyons which correspond to classical trajectories interpolating from multiple, small fuzzy spheres to a single, large sphere. We briefly discuss spatially independent configurations of a D3/D5 system described by the same matrix model which now possesses a supergravity dual.Comment: 26 pages, 3 figures, uses JHEP.cls; (v2) references adde

Exploring the vicinity of the Bogomol'nyi-Prasad-Sommerfield bound

We investigate systems of real scalar fields in bidimensional spacetime, dealing with potentials that are small modifications of potentials that admit supersymmetric extensions. The modifications are controlled by a real parameter, which allows implementing a perturbation procedure when such parameter is small. The approach allows obtaining the energy and topological charge in closed forms, up to first order in the parameter. We illustrate the procedure with some examples. In particular, we show how to remove the degeneracy in energy for the one-field and the two-field solutions that appear in a model of two real scalar fields.Comment: Revtex, 9 pages, To be published in J. Phys.

Nonabelian gauge field and dual description of fuzzy sphere

In matrix models, higher dimensional D-branes are obtained by imposing a noncommutative relation to coordinates of lower dimensional D-branes. On the other hand, a dual description of this noncommutative space is provided by higher dimensional D-branes with gauge fields. Fuzzy spheres can appear as a configuration of lower dimensional D-branes in a constant R-R field strength background. In this paper, we consider a dual description of higher dimensional fuzzy spheres by introducing nonabelian gauge fields on higher dimensional spherical D-branes. By using the Born-Infeld action, we show that a fuzzy $2k$-sphere and spherical D$2k$-branes with a nonabelian gauge field whose Chern character is nontrivial are the same objects when $n$ is large. We discuss a relationship between the noncommutative geometry and nonabelian gauge fields. Nonabelian gauge fields are represented by noncommutative matrices including the coordinate dependence. A similarity to the quantum Hall system is also studied.Comment: 28 page

BPS black holes in N=2 D=4 gauged supergravities

We construct and analyze BPS black hole solutions in gauged N=2, D=4 supergravity with charged hypermultiplets. A class of solutions can be found through spontaneous symmetry breaking in vacua that preserve maximal supersymmetry. The resulting black holes do not carry any hair for the scalars. We demonstrate this with explicit examples of both asymptotically flat and anti-de Sitter black holes. Next, we analyze the BPS conditions for asymptotically flat black holes with scalar hair and spherical or axial symmetry. We find solutions only in cases when the metric contains ripples and the vector multiplet scalars become ghost-like. We give explicit examples that can be analyzed numerically. Finally, we comment on a way to circumvent the ghost-problem by introducing also fermionic hair.Comment: 40 pages, 2 figures; v2 references added; v3 minor changes, published versio

Massive Gravity Theories and limits of Ghost-free Bigravity models

We construct a class of theories which extend New Massive Gravity to higher orders in curvature in any dimension. The lagrangians arise as limits of a new class of bimetric theories of Lovelock gravity, which are unitary theories free from the Boulware-Deser ghost. These Lovelock bigravity models represent the most general non-chiral ghost-free theories of an interacting massless and massive spin-two field in any dimension. The scaling limit is taken in such a way that unitarity is explicitly broken, but the Boulware-Deser ghost remains absent. This automatically implies the existence of a holographic $c$-theorem for these theories. We also show that the Born-Infeld extension of New Massive Gravity falls into our class of models demonstrating that this theory is also free of the Boulware-Deser ghost. These results extend existing connections between New Massive Gravity, bigravity theories, Galileon theories and holographic $c$-theorems.Comment: 11+5 page