Near Horizon Geometry of Strings Ending on Intersecting D8/D4-branes

We consider solutions of massive IIA supergravity corresponding to the half-BPS intersection of D8/D4-branes with fundamental strings. The $1+1$-dimensional intersection preserves the symmetry $D(2,1;\gamma;1) \times SO(4)$. We give a reduction and partial integration of the BPS equations for this symmetry group. We then specialize to the cases of enhanced supersymmetry corresponding to $\gamma = -1/2,-2$ or $\gamma = 1$. In the first case, we show that the only solution with enhanced symmetry is given by the $AdS_6$ geometry describing the near horizon geometry of D8/D4-branes in the presence of an O8-plane. In the second case, we identify novel solutions corresponding to fundamental strings ending on D8-branes and a second set of novel solutions corresponding to fundamental strings ending on an O8-plane. In both cases, the fundamental string geometry contains an asymptotically flat region where the string coupling goes to zero. We also show that there are no solutions corresponding to $1+0$-dimensional CFTs, which one may have hoped to construct by suspending fundamental strings between D8-branes.Comment: 36 pages, 6 figures (12 pdf figure files

Exact Half-BPS Flux Solutions in M-theory with D(2,1;c′;0)2D(2, 1; c'; 0)^2 Symmetry: Local Solutions

We construct local solutions to 11-dimensional supergravity (or M-theory), which are invariant under the superalgebra $D(2, 1; c'; 0)\oplus D(2, 1; c'; 0)$ for all values of the parameter $c'$. The BPS constraints are reduced to a single linear PDE on a complex function $G$. The PDE was solved in 0806.0605 modulo application of boundary and regularity conditions. The physical fields of the solutions are determined by $c'$, a harmonic function $h$, and the complex function $G$. $h$ and $G$ are both functions on a 2-dimensional compact Riemannian manifold. The harmonic function $h$ is freely chosen. We obtain the expressions for the metric and the field strength in terms of $G$, $h$, and $c'$ and show that these are indeed valid solutions of the Einstein, Maxwell, and Bianchi equations. Finally we give a construction of one parameter deformations of $AdS_7 \times S^4$ and $AdS_4 \times S^7$ as a function of $c'$

Decays of near BPS heterotic strings

The decay of highly excited massive string states in compactified heterotic string theories is discussed. We calculate the decay rate and spectrum of states carrying momentum and winding in the compactified direction. The longest lived states in the spectrum are near BPS states whose decay is dominated by a single decay channel of massless radiation which brings the state closer to being BPS.Comment: 28 pages, harvmac, 3 figure

Exact Half-BPS Flux Solutions in M-theory I, Local Solutions

The complete eleven-dimensional supergravity solutions with 16 supersymmetries on manifolds of the form $AdS_3 \times S^3 \times S^3 \times \Sigma$, with isometry $SO(2,2) \times SO(4) \times SO(4)$, and with either $AdS_4 \times S^7$ or $AdS_7 \times S^4$ boundary behavior, are obtained in exact form. The two-dimensional parameter space $\Sigma$ is a Riemann surface with boundary, over which the product space $AdS_3 \times S^3 \times S^3$ is warped. By mapping the reduced BPS equations to an integrable system of the sine-Gordon/Liouville type, and then mapping this integrable system onto a linear equation, the general local solutions are constructed explicitly in terms of one harmonic function on $\Sigma$, and an integral transform of two further harmonic functions on $\Sigma$. The solutions to the BPS equations are shown to automatically solve the Bianchi identities and field equations for the 4-form field, as well as Einstein's equations. The solutions we obtain have non-vanishing 4-form field strength on each of the three factors of $AdS_3 \times S^3 \times S^3$, and include fully back-reacted M2-branes in $AdS_7 \times S^4$ and M5-branes in $AdS_4 \times S^7$. No interpolating solutions exist with mixed $AdS_4 \times S^7$ and $AdS_7 \times S^4$ boundary behavior. Global regularity of these local solutions, as well as the existence of further solutions with neither $AdS_4 \times S^7$ nor $AdS_7 \times S^4$ boundary behavior will be studied elsewhere.Comment: 62 pages, 2 figures, references and clarifications on supergroups adde

M-theory Solutions Invariant under D(2,1;γ)⊕D(2,1;γ)D(2,1;\gamma) \oplus D(2,1;\gamma)

We simplify and extend the construction of half-BPS solutions to 11-dimensional supergravity, with isometry superalgebra D(2,1;\gamma) \oplus D(2,1;\gamma). Their space-time has the form AdS_3 x S^3 x S^3 warped over a Riemann surface \Sigma. It describes near-horizon geometries of M2 branes ending on, or intersecting with, M5 branes along a common string. The general solution to the BPS equations is specified by a reduced set of data (\gamma, h, G), where \gamma is the real parameter of the isometry superalgebra, and h and G are functions on \Sigma whose differential equations and regularity conditions depend only on the sign of \gamma. The magnitude of \gamma enters only through the map of h, G onto the supergravity fields, thereby promoting all solutions into families parametrized by |\gamma|. By analyzing the regularity conditions for the supergravity fields, we prove two general theorems: (i) that the only solution with a 2-dimensional CFT dual is AdS_3 x S^3 x S^3 x R^2, modulo discrete identifications of the flat R^2, and (ii) that solutions with \gamma < 0 cannot have more than one asymptotic higher-dimensional AdS region. We classify the allowed singularities of h and G near the boundary of \Sigma, and identify four local solutions: asymptotic AdS_4/Z_2 or AdS_7' regions; highly-curved M5-branes; and a coordinate singularity called the "cap". By putting these "Lego" pieces together we recover all known global regular solutions with the above symmetry, including the self-dual strings on M5 for $\gamma < 0$, and the Janus solution for \gamma > 0, but now promoted to families parametrized by |\gamma|. We also construct exactly new regular solutions which are asymptotic to AdS_4/Z_2 for \gamma < 0, and conjecture that they are a different superconformal limit of the self-dual string.Comment: 61 pages, 6 figures, references and acknowledgments added in version

Wilson Surface Central Charge from Holographic Entanglement Entropy

We use entanglement entropy to define a central charge associated to a two-dimensional defect or boundary in a conformal field theory (CFT). We present holographic calculations of this central charge for several maximally supersymmetric CFTs dual to eleven-dimensional supergravity in Anti-de Sitter space, namely the M5-brane theory with a Wilson surface defect and three-dimensional CFTs related to the M2-brane theory with a boundary. Our results for the central charge depend on a partition of the number of M2-branes, $N$, ending on the number of M5-branes, $M$. For the Wilson surface, the partition specifies a representation of the gauge algebra, and we write our result for the central charge in a compact form in terms of the algebra's Weyl vector and the representation's highest weight vector. We explore how the central charge scales with $N$ and $M$ for some examples of partitions. In general the central charge does not scale as $M^3$ or $N^{3/2}$, the number of degrees of freedom of the M5- or M2-brane theory at large $M$ or $N$, respectively.Comment: 51 pages, 7 figure

Half-BPS supergravity solutions and superalgebras

We establish a correspondence between certain Lie superalgebras with 16 fermionic generators, and half-BPS solutions to supergravities with 32 supersymmetries. Three cases are discussed. For Type IIB supergravity, we relate semi-simple Lie superalgebras H with 16 fermionic generators which are subalgebras of PSU(2,2|4), to families of half-BPS solutions which are invariant under H, and locally asymptotic to AdS_5 x S^5. Similarly, for M-theory, we relate semi-simple Lie superalgebras H with 16 fermionic generators which are subalgebras of OSp(8^*|4) or OSp(8|4,R) to families of half-BPS solutions which are invariant under H, and locally asymptotic to AdS_7 x S^4 or AdS_4 x S^7 respectively. Possible enhancements to more than 16 supersymmetries, such as 24, are also analyzed. The classification of semi-simple subalgebras of PSU(2,2|4), OSp(8^*|4), and OSp(8|4,R) derived in this paper, leads us to conjecture the existence of various new families of half-BPS solutions to Type IIB supergravity and M-theory.Comment: 85 pages, 1 figure, 19 tables. In v2, references added; various corrections and extensive revisions and clarifications made in section 5 and appendix

String Junctions and Holographic Interfaces

In this paper we study half-BPS type IIB supergravity solutions with multiple $AdS_3\times S^3\times M_4$ asymptotic regions, where $M_4$ is either $T^4$ or $K_3$. These solutions were first constructed in [1] and have geometries given by the warped product of $AdS_2 \times S^2 \times M_4$ over $\Sigma$, where $\Sigma$ is a Riemann surface. We show that the holographic boundary has the structure of a star graph, i.e. $n$ half-lines joined at a point. The attractor mechanism and the relation of the solutions to junctions of self-dual strings in six-dimensional supergravity are discussed. The solutions of [1] are constructed introducing two meromorphic and two harmonic functions defined on $\Sigma$. We focus our analysis on solutions corresponding to junctions of three different conformal field theories and show that the conditions for having a solution charged only under Ramond-Ramond three-form fields reduce to relations involving the positions of the poles and the residues of the relevant harmonic and meromorphic functions. The degeneration limit in which some of the poles collide is analyzed in detail. Finally, we calculate the holographic boundary entropy for a junction of three CFTs and obtain a simple expression in terms of poles and residues.Comment: 54 pages, 6 figures, pdf-LaTeX, v2: minor change

Exact Half-BPS Flux Solutions in M-theory III: Existence and rigidity of global solutions asymptotic to AdS4 x S7

The BPS equations in M-theory for solutions with 16 residual supersymmetries, $SO(2,2)\times SO(4)\times SO(4)$ symmetry, and $AdS_4 \times S^7$ asymptotics, were reduced in [arXiv:0806.0605] to a linear first order partial differential equation on a Riemann surface with boundary, subject to a non-trivial quadratic constraint. In the present paper, suitable regularity and boundary conditions are imposed for the existence of global solutions. We seek regular solutions with multiple distinct asymptotic $AdS_4 \times S^7$ regions, but find that, remarkably, such solutions invariably reduce to multiple covers of the M-Janus solution found by the authors in [arXiv:0904.3313], suggesting rigidity of the half-BPS M-Janus solution. In particular, we prove analytically that no other smooth deformations away from the M-Janus solution exist, as such deformations invariably violate the quadratic constraint. These rigidity results are contrasted to the existence of half-BPS solutions with non-trivial 4-form fluxes and charges asymptotic to $AdS_7 \times S^4$. The results are related to the possibility of M2-branes to end on M5-branes, but the impossibility of M5-branes to end on M2-branes, and to the non-existence of half-BPS solutions with simultaneous $AdS_4 \times S^7$ and $AdS_7 \times S^4$ asymptotic regions.Comment: 52 pages, 2 figures, pdf-latex. Minor change