Fractional branes, warped compactifications and backreacted orientifold planes

The standard extremal p-brane solutions in supergravity are known to allow for a generalisation which consists of adding a linear dependence on the world-volume coordinates to the usual harmonic function. In this note we demonstrate that remarkably this generalisation goes through in exactly the same way for p-branes with fluxes added to it that correspond to fractional p-branes. We relate this to warped orientifold compactifications by trading the Dp-branes for Op-planes that solve the RR tadpole condition. This allows us to interpret the worldvolume dependence as due to lower-dimensional scalars that flow along the massless directions in the no-scale potential. Depending on the details of the fluxes these flows can be supersymmetric domain wall flows. Our solutions provide explicit examples of backreacted orientifold planes in compactifications with non-constant moduli.Comment: 20 pages, incl. references. v2: small changes required for JHEP publication. v3: few equation typos correcte

The problematic backreaction of SUSY-breaking branes

In this paper we investigate the localisation of SUSY-breaking branes which, in the smeared approximation, support specific non-BPS vacua. We show, for a wide class of boundary conditions, that there is no flux vacuum when the branes are described by a genuine delta-function. Even more, we find that the smeared solution is the unique solution with a regular brane profile. Our setup consists of a non-BPS AdS_7 solution in massive IIA supergravity with smeared anti-D6-branes and fluxes T-dual to ISD fluxes in IIB supergravity.Comment: 27 pages, Latex2e, 5 figure

(Anti-)Brane backreaction beyond perturbation theory

We improve on the understanding of the backreaction of anti-D6-branes in a flux background that is mutually BPS with D6-branes. This setup is analogous to the study of the backreaction of anti-D3-branes inserted in the KS throat, but does not require us to smear the anti-branes or do a perturbative analysis around the BPS background. We solve the full equations of motion near the anti-D6-branes and show that only two boundary conditions are consistent with the equations of motion. Upon invoking a topological argument we eliminate the boundary condition with regular H flux since it cannot lead to a solution that approaches the right kind of flux away from the anti-D6-brane. This leaves us with a boundary condition which has singular, but integrable, H flux energy density.Comment: 12 pages + appendices, 1 figure; v2: minor changes, version published in JHE

Wall Crossing, Quivers and Crystals

We study the spectrum of BPS D-branes on a Calabi-Yau manifold using the 0+1 dimensional quiver gauge theory that describes the dynamics of the branes at low energies. The results of Kontsevich and Soibelman predict how the degeneracies change. We argue that Seiberg dualities of the quiver gauge theories, which change the basis of BPS states, correspond to crossing the "walls of the second kind." There is a large class of examples, including local del Pezzo surfaces, where the BPS degeneracies of quivers corresponding to one D6 brane bound to arbitrary numbers of D4, D2 and D0 branes are counted by melting crystal configurations. We show that the melting crystals that arise are a discretization of the Calabi-Yau geometry. The shape of the crystal is determined by the Calabi-Yau geometry and the background B-field, and its microscopic structure by the quiver Q. We prove that the BPS degeneracies computed from Q and Q' are related by the Kontsevich Soibelman formula, using a geometric realization of the Seiberg duality in the crystal. We also show that, in the limit of infinite B-field, the combinatorics of crystals arising from the quivers becomes that of the topological vertex. We thus re-derive the Gromov-Witten/Donaldson-Thomas correspondence

Phases of planar 5-dimensional supersymmetric Chern-Simons theory

In this paper we investigate the large-$N$ behavior of 5-dimensional $\mathcal{N}=1$ super Yang-Mills with a level $k$ Chern-Simons term and an adjoint hypermultiplet. As in three-dimensional Chern-Simons theories, one must choose an integration contour to completely define the theory. Using localization, we reduce the path integral to a matrix model with a cubic action and compute its free energy in various scenarios. In the limit of infinite Yang-Mills coupling and for particular choices of the contours, we find that the free-energy scales as $N^{5/2}$ for $U(N)$ gauge groups with large values of the Chern-Simons 't\,Hooft coupling, $\tilde\lambda\equiv N/k$. If we also set the hypermultiplet mass to zero, then this limit is a superconformal fixed point and the $N^{5/2}$ behavior parallels other fixed points which have known supergravity duals. We also demonstrate that $SU(N)$ gauge groups cannot have this $N^{5/2}$ scaling for their free-energy. At finite Yang-Mills coupling we establish the existence of a third order phase transition where the theory crosses over from the Yang-Mills phase to the Chern-Simons phase. The phase transition exists for any value of $\tilde\lambda$, although the details differ between small and large values of $\tilde\lambda$. For pure Chern-Simons theories we present evidence for a chain of phase transitions as $\tilde\lambda$ is increased. We also find the expectation values for supersymmetric circular Wilson loops in these various scenarios and show that the Chern-Simons term leads to different physical properties for fundamental and anti-fundamental Wilson loops. Different choices of the integration contours also lead to different properties for the loops.Comment: 40 pages, 17 figures, Minor corrections, Published versio

Localisation and origin of the bacteriochlorophyll-derived photosensitizer in the retina of the deep-sea dragon fish Malacosteus niger

Most deep-sea fish have a single visual pigment maximally sensitive at short wavelengths, approximately matching the spectrum of both downwelling sunlight and bioluminescence. However, Malcosteus niger produces far-red bioluminescence and its longwave retinal sensitivity is enhanced by red-shifted visual pigments, a longwave reflecting tapetum and, uniquely, a bacteriochlorophyllderived photosensitizer. The origin of the photosensitizer, however, remains unclear. We investigated whether the bacteriochlorophyll was produced by endosymbiotic bacteria within unusual structures adjacent to the photoreceptors that had previously been described in this species. However, microscopy, elemental analysis and SYTOX green staining provided no evidence for such localised retinal bacteria, instead the photosensitizer was shown to be distributed throughout the retina. Furthermore, comparison of mRNA from the retina of Malacosteus to that of the closely related Pachystomias microdon (which does not contain a bacterichlorophyll-derived photosensitzer) revealed no genes of bacterial origin that were specifically up-regulated in Malacosteus. Instead up-regulated Malacosteus genes were associated with photosensitivity and may relate to its unique visual ecology and the chlorophyll-based visual system. We also suggest that the unusual longwave-reflecting, astaxanthin-based, tapetum of Malacosteus may protect the retina from the potential cytotoxicity of such a system

Gravity waves and the LHC: Towards high-scale inflation with low-energy SUSY

It has been argued that rather generic features of string-inspired inflationary theories with low-energy supersymmetry (SUSY) make it difficult to achieve inflation with a Hubble scale H > m_{3/2}, where m_{3/2} is the gravitino mass in the SUSY-breaking vacuum state. We present a class of string-inspired supergravity realizations of chaotic inflation where a simple, dynamical mechanism yields hierarchically small scales of post-inflationary supersymmetry breaking. Within these toy models we can easily achieve small ratios between m_{3/2} and the Hubble scale of inflation. This is possible because the expectation value of the superpotential relaxes from large to small values during the course of inflation. However, our toy models do not provide a reasonable fit to cosmological data if one sets the SUSY-breaking scale to m_{3/2} < TeV. Our work is a small step towards relieving the apparent tension between high-scale inflation and low-scale supersymmetry breaking in string compactifications.Comment: 21+1 pages, 5 figures, LaTeX, v2: added references, v3: very minor changes, version to appear in JHE

Connecting the Holographic and Wilsonian Renormalization Groups

Inspired by the AdS/CFT correspondence, we develop an explicit formal duality between the planar limit of a d-dimensional gauge theory and a classical field theory in a (d+1)-dimensional anti-de Sitter space. The key ingredient is the identification of fields in AdS with generalized Hubbard-Stratonovich transforms of single-trace couplings of the QFT. We show that the Wilsonian renormalization group flow of these transformed couplings matches the holographic (Hamilton-Jacobi) flow of bulk fields along the radial direction in AdS. This result allows one to outline an AdS/CFT dictionary that does not rely on string theory.Comment: 11 pages, 1 figure; metadata modified in v2; added references and minor changes in v3; v4 as published in JHE

Quiver Structure of Heterotic Moduli

We analyse the vector bundle moduli arising from generic heterotic compactifications from the point of view of quiver representations. Phenomena such as stability walls, crossing between chambers of supersymmetry, splitting of non-Abelian bundles and dynamic generation of D-terms are succinctly encoded into finite quivers. By studying the Poincar\'e polynomial of the quiver moduli space using the Reineke formula, we can learn about such useful concepts as Donaldson-Thomas invariants, instanton transitions and supersymmetry breaking.Comment: 38 pages, 5 figures, 1 tabl

D-brane Charges in Gravitational Duals of 2+1 Dimensional Gauge Theories and Duality Cascades

We perform a systematic analysis of the D-brane charges associated with string theory realizations of d=3 gauge theories, focusing on the examples of the N=4 supersymmetric U(N)xU(N+M) Yang-Mills theory and the N=3 supersymmetric U(N)xU(N+M) Yang-Mills-Chern-Simons theory. We use both the brane construction of these theories and their dual string theory backgrounds in the supergravity approximation. In the N=4 case we generalize the previously known gravitational duals to arbitrary values of the gauge couplings, and present a precise mapping between the gravity and field theory parameters. In the N=3 case, which (for some values of N and M) flows to an N=6 supersymmetric Chern-Simons-matter theory in the IR, we argue that the careful analysis of the charges leads to a shift in the value of the B-field in the IR solution by 1/2, in units where its periodicity is one, compared to previous claims. We also suggest that the N=3 theories may exhibit, for some values of N and M, duality cascades similar to those of the Klebanov-Strassler theory.Comment: 47 pages, 9 figures; minor changes, references adde