Massless particles on supergroups and AdS3 x S3 supergravity

Firstly, we study the state space of a massless particle on a supergroup with a reparameterization invariant action. After gauge fixing the reparameterization invariance, we compute the physical state space through the BRST cohomology and show that the quadratic Casimir Hamiltonian becomes diagonalizable in cohomology. We illustrate the general mechanism in detail in the example of a supergroup target GL(1|1). The space of physical states remains an indecomposable infinite dimensional representation of the space-time supersymmetry algebra. Secondly, we show how the full string BRST cohomology in the particle limit of string theory on AdS3 x S3 renders the quadratic Casimir diagonalizable, and reduces the Hilbert space to finite dimensional representations of the space-time supersymmetry algebra (after analytic continuation). Our analysis provides an efficient way to calculate the Kaluza-Klein spectrum for supergravity on AdS3 x S3. It may also be a step towards the identification of an interesting and simpler subsector of logarithmic supergroup conformal field theories, relevant to string theory.Comment: 16 pages, 10 figure

3D N=6 Gauged Supergravity: Admissible Gauge Groups, Vacua and RG Flows

We study N=6 gauged supergravity in three dimensions with scalar manifolds $\frac{SU(4,k)}{S(U(4)\times U(k))}$ for $k=1,2,3,4$ in great details. We classify some admissible non-compact gauge groups which can be consistently gauged and preserve all supersymmetries. We give the explicit form of the embedding tensors for these gauge groups as well as study their scalar potentials on the full scalar manifold for each value of $k=1,2,3,4$ along with the corresponding vacua. Furthermore, the potentials for the compact gauge groups, $SO(p)\times SO(6-p)\times SU(k)\times U(1)$ for $p=3,4,5,6$, identified previously in the literature are partially studied on a submanifold of the full scalar manifold. This submanifold is invariant under a certain subgroup of the corresponding gauge group. We find a number of supersymmetric AdS vacua in the case of compact gauge groups. We then consider holographic RG flow solutions in the compact gauge groups $SO(6)\times SU(4)\times U(1)$ and $SO(4)\times SO(2)\times SU(4)\times U(1)$ for the k=4 case. The solutions involving one active scalar can be found analytically and describe operator flows driven by a relevant operator of dimension 3/2. For non-compact gauge groups, we find all types of vacua namely AdS, Minkowski and dS, but there is no possibility of RG flows in the AdS/CFT sense for all gauge groups considered here.Comment: 43 pages, no figures references added, typoes corrected and more information adde

Universality and exactness of Schrodinger geometries in string and M-theory

We propose an organizing principle for classifying and constructing Schrodinger-invariant solutions within string theory and M-theory, based on the idea that such solutions represent nonlinear completions of linearized vector and graviton Kaluza-Klein excitations of AdS compactifications. A crucial simplification, derived from the symmetry of AdS, is that the nonlinearities appear only quadratically. Accordingly, every AdS vacuum admits infinite families of Schrodinger deformations parameterized by the dynamical exponent z. We exhibit the ease of finding these solutions by presenting three new constructions: two from M5 branes, both wrapped and extended, and one from the D1-D5 (and S-dual F1-NS5) system. From the boundary perspective, perturbing a CFT by a null vector operator can lead to nonzero beta-functions for spin-2 operators; however, symmetry restricts them to be at most quadratic in couplings. This point of view also allows us to easily prove nonrenormalization theorems: for any Sch(z) solution of two-derivative supergravity constructed in the above manner, z is uncorrected to all orders in higher derivative corrections if the deforming KK mode lies in a short multiplet of an AdS supergroup. Furthermore, we find infinite classes of 1/4 BPS solutions with 4-,5- and 7-dimensional Schrodinger symmetry that are exact.Comment: 31 pages, plus appendices; v2, minor corrections, added refs, slight change in interpretation in section 2.3, new Schrodinger and Lifshitz solutions included; v3, clarifications in sections 2 and 3 regarding existence of solutions and multi-trace operator

Kerr/CFT, dipole theories and nonrelativistic CFTs

We study solutions of type IIB supergravity which are SL(2,R) x SU(2) x U(1)^2 invariant deformations of AdS_3 x S^3 x K3 and take the form of products of self-dual spacelike warped AdS_3 and a deformed three-sphere. One of these backgrounds has been recently argued to be relevant for a derivation of Kerr/CFT from string theory, whereas the remaining ones are holographic duals of two-dimensional dipole theories and their S-duals. We show that each of these backgrounds is holographically dual to a deformation of the DLCQ of the D1-D5 CFT by a specific supersymmetric (1,2) operator, which we write down explicitly in terms of twist operators at the free orbifold point. The deforming operator is argued to be exactly marginal with respect to the zero-dimensional nonrelativistic conformal (or Schroedinger) group - which is simply SL(2,R)_L x U(1)_R. Moreover, in the supergravity limit of large N and strong coupling, no other single-trace operators are turned on. We thus propose that the field theory duals to the backgrounds of interest are nonrelativistic CFTs defined by adding the single Schroedinger-invariant (1,2) operator mentioned above to the original CFT action. Our analysis indicates that the rotating extremal black holes we study are best thought of as finite right-moving temperature (non-supersymmetric) states in the above-defined supersymmetric nonrelativistic CFT and hints towards a more general connection between Kerr/CFT and two-dimensional non-relativistic CFTs.Comment: 48+8 pages, 4 figures; minor corrections and references adde

Holographic 4-point correlators with heavy states

SCOAP

Correlators at large c without information loss

SCOAP

Concurrence of form and function in developing networks and its role in synaptic pruning

A fundamental question in neuroscience is how structure and function of neural systems are related. We study this interplay by combining a familiar auto-associative neural network with an evolving mechanism for the birth and death of synapses. A feedback loop then arises leading to two qualitatively different types of behaviour. In one, the network structure becomes heterogeneous and dissasortative, and the system displays good memory performance; furthermore, the structure is optimised for the particular memory patterns stored during the process. In the other, the structure remains homogeneous and incapable of pattern retrieval. These findings provide an inspiring picture of brain structure and dynamics that is compatible with experimental results on early brain development, and may help to explain synaptic pruning. Other evolving networks—such as those of protein interactions—might share the basic ingredients for this feedback loop and other questions, and indeed many of their structural features are as predicted by our model.We are grateful for financial support from the Spanish MINECO (project of Excellence: FIS2017-84256-P) and from “Obra Social La Caixa”