Holographic renormalization and supersymmetry

Holographic renormalization is a systematic procedure for regulating divergences in observables in asymptotically locally AdS spacetimes. For dual boundary field theories which are supersymmetric it is natural to ask whether this defines a supersymmetric renormalization scheme. Recent results in localization have brought this question into sharp focus: rigid supersymmetry on a curved boundary requires specific geometric structures, and general arguments imply that BPS observables, such as the partition function, are invariant under certain deformations of these structures. One can then ask if the dual holographic observables are similarly invariant. We study this question in minimal N = 2 gauged supergravity in four and five dimensions. In four dimensions we show that holographic renormalization precisely reproduces the expected field theory results. In five dimensions we find that no choice of standard holographic counterterms is compatible with supersymmetry, which leads us to introduce novel finite boundary terms. For a class of solutions satisfying certain topological assumptions we provide some independent tests of these new boundary terms, in particular showing that they reproduce the expected VEVs of conserved charges

The holographic supersymmetric Casimir energy

We consider a general class of asymptotically locally AdS5 solutions of minimal gauged supergravity, that are dual to superconformal field theories on curved backgrounds S 1 × M3 preserving two supercharges. We demonstrate that standard holographic renormalization corresponds to a scheme that breaks supersymmetry. We propose new boundary terms that restore supersymmetry, and show that for smooth solutions with topology S 1 ×R 4 the improved on-shell action reproduces both the supersymmetric Casimir energy and the field theory BPS relation between charges

Nonlinear Klein-Gordon-Maxwell systems with Neumann boundary conditions on a Riemannian manifold with boundary

Let (M,g) be a smooth compact, n dimensional Riemannian manifold, n=3,4 with smooth n-1 dimensional boundary. We search the positive solutions of the singularly perturbed Klein Gordon Maxwell Proca system with homogeneous Neumann boundary conditions or for the singularly perturbed Klein Gordon Maxwell system with mixed Dirichlet Neumann homogeneous boundary conditions. We prove that stable critical points of the mean curvature of the boundary generates solutions when the perturbation parameter is sufficiently small.Comment: arXiv admin note: text overlap with arXiv:1410.884

de Sitter Supersymmetry Revisited

We present the basic $\mathcal{N} =1$ superconformal field theories in four-dimensional de Sitter space-time, namely the non-abelian super Yang-Mills theory and the chiral multiplet theory with gauge interactions or cubic superpotential. These theories have eight supercharges and are invariant under the full $SO(4,2)$ group of conformal symmetries, which includes the de Sitter isometry group $SO(4,1)$ as a subgroup. The theories are ghost-free and the anti-commutator $\sum_\alpha\{Q_\alpha, Q^{\alpha\dagger}\}$ is positive. SUSY Ward identities uniquely select the Bunch-Davies vacuum state. This vacuum state is invariant under superconformal transformations, despite the fact that de Sitter space has non-zero Hawking temperature. The $\mathcal{N}=1$ theories are classically invariant under the $SU(2,2|1)$ superconformal group, but this symmetry is broken by radiative corrections. However, no such difficulty is expected in the $\mathcal{N}=4$ theory, which is presented in appendix B.Comment: 21 pages, 2 figure

Holographic renormalization and supersymmetry

Holographic renormalization is a systematic procedure for regulating divergences in observables in asymptotically locally AdS spacetimes. For dual boundary field theories which are supersymmetric it is natural to ask whether this defines a supersymmetric renormalization scheme. Recent results in localization have brought this question into sharp focus: rigid supersymmetry on a curved boundary requires specific geometric structures, and general arguments imply that BPS observables, such as the partition function, are invariant under certain deformations of these structures. One can then ask if the dual holographic observables are similarly invariant. We study this question in minimal N = 2 gauged supergravity in four and five dimensions. In four dimensions we show that holographic renormalization precisely reproduces the expected field theory results. In five dimensions we find that no choice of standard holographic counterterms is compatible with supersymmetry, which leads us to introduce novel finite boundary terms. For a class of solutions satisfying certain topological assumptions we provide some independent tests of these new boundary terms, in particular showing that they reproduce the expected VEVs of conserved charges.Comment: 70 pages; corrected typo

The critical dimension for a 4th order problem with singular nonlinearity

We study the regularity of the extremal solution of the semilinear biharmonic equation \bi u=\f{\lambda}{(1-u)^2}, which models a simple Micro-Electromechanical System (MEMS) device on a ball B\subset\IR^N, under Dirichlet boundary conditions $u=\partial_\nu u=0$ on $\partial B$. We complete here the results of F.H. Lin and Y.S. Yang \cite{LY} regarding the identification of a "pull-in voltage" \la^*>0 such that a stable classical solution u_\la with 0 exists for \la\in (0,\la^*), while there is none of any kind when \la>\la^*. Our main result asserts that the extremal solution $u_{\lambda^*}$ is regular $(\sup_B u_{\lambda^*} <1)$ provided $N \le 8$ while $u_{\lambda^*}$ is singular ($\sup_B u_{\lambda^*} =1$) for $N \ge 9$, in which case $1-C_0|x|^{4/3}\leq u_{\lambda^*} (x) \leq 1-|x|^{4/3}$ on the unit ball, where $C_0:= (\frac{\lambda^*}{\overline{\lambda}})^{1/3}$ and $\bar{\lambda}:= {8/9} (N-{2/3}) (N- {8/3})$.Comment: 19 pages. This paper completes and replaces a paper (with a similar title) which appeared in arXiv:0810.5380. Updated versions --if any-- of this author's papers can be downloaded at this http://www.birs.ca/~nassif

New Compactifications of Eleven Dimensional Supergravity

Using canonical forms on S^7, viewed as an SU(2) bundle over S^4, we introduce consistent ansatze for the 4-form field strength of eleven-dimensional supergravity and rederive the known squashed, stretched, and the Englert solutions. Further, by rewriting the metric of S^7 as a U(1) bundle over CP^3, we present yet more general ansatze. As a result, we find a new compactifying solution of the type AdS_5\times CP^3, where CP^3 is stretched along its S^2 fiber. We also find a new solution of AdS_2\times H^2\times S^7 type in Euclidean space.Comment: 15 pages, revised sec. 4, included new CP^3 and S^7 compactifications, published versio

The receptor-binding sequence of urokinase. A biological function for the growth-factor module of proteases.

Previous studies have shown that the region of human urokinase-type plasminogen activator (uPA) responsible for receptor binding resides in the amino-terminal fragment (ATF, residues 1-135) (Stoppelli, M.P., Corti, A., Soffientini, A., Cassani, G., Blasi, F., and Assoian, R.K. (1985) Proc. Natl. Acad. Sci. U.S. A. 82, 4939-4943). The area within ATF responsible for specific receptor binding has now been identified by the ability of different synthetic peptides corresponding to different regions of the amino terminus of uPA to inhibit receptor binding of 125I-labeled ATF. A peptide corresponding to human [Ala19]uPA-(12-32) resulted in 50% inhibition of ATF binding at 100 nM. Peptides uPA-(18-32) and [Ala13]uPA-(9-20) inhibit at 100 and 2000 microM, respectively. The human peptide uPA-(1-14) and the mouse peptide [Ala20]uPA-(13-33) have no effect on ATF receptor binding. This region of uPA is referred to as the growth factor module since it shares partial amino acid sequence homology (residues 14-33) to epidermal growth factor (EGF). Furthermore, this region of EGF is responsible for binding of EGF to its receptor (Komoriya, A. Hortsch, M., Meyers, C., Smith, M., Kanety, H., and Schlessinger, J. (1984) Proc. Natl. Acad. Sci. U.S.A. 81, 1351-1355). However, EGF does not inhibit ATF receptor binding. Comparison of the sequences responsible for receptor binding of uPA and EGF indicate that the region of highest homology is between residues 13-19 and 14-20 of human uPA and EGF, respectively. In addition, there is a conservation of the spacings of four cysteines in this module whereas there is no homology between residues 20-30 and 21-33 of uPA and EGF. Thus, residues 20-30 of uPA apparently confer receptor binding specificity, and residues 13-19 provide the proper conformation to the adjacent binding region