On matter coupled to the higher spin square

Gaberdiel and Gopakumar recently proposed that the tensionless limit of string theory on $AdS_3 \times S^3 \times T^4$ takes the form of a higher spin theory with a gauge algebra that is referred to as the higher spin square. In this note, we formulate the linearized Vasiliev-type equations which describe a matter field coupled to the higher spin square. We study the particle spectrum of this field and show that it accounts for the entire untwisted sector of the dual symmetric orbifold CFT, thereby confirming a conjecture by Gaberdiel and Gopakumar. In doing so, we pinpoint the group-theoretic data which determine the spectrum of a matter field coupled to a general higher spin algebra, which we illustrate by revisiting the theory based on the $hs[1/2]$ algebra.Comment: 18 pages. V2: minor changes, reference adde

Some properties of the spinor fourier transform

In this paper, the theory of the spinor Fourier transform introduced in [Batard T, Berthier M, Saint-Jean C, Clifford-Fourier Transform for Color Image Processing, Geometric Algebra Computing for Engineering and Computer Science (E. Bayro-Corrochano and G. Scheuermann Eds.), Springer, London, 2010, pp. 135–161] is further developed. While in the original paper, the transform was determined for vector-valued functions only, it now will be extended to functions taking values in the entire Clifford algebra. Next, two bases are determined under which this Fourier transform is diagonalizable. A main stumbling block for further applications, in particular concerning filter design in the Fourier domain, is the lack of a proper convolution theorem. This problem will be tackled in the final section of this paper

Models for some irreducible representations of so(m,C) in discrete Clifford analysis

In this paper we work in the `split' discrete Clifford analysis setting, i.e. the m-dimensional function theory concerning null-functions of the discrete Dirac operator d, defined on the grid Zm, involving both forward and backward differences. This Dirac operator factorizes the (discrete) Star-Laplacian (Delta*= d2). We show how the space Hk of discrete k-homogeneous spherical harmonics, which is a reducible so(m;C)-representation, may explicitly be decomposed into 2^2m isomorphic copies of irreducible so(m;C)-representations with highest weight (k, 0, ..., 0). The key element is the introduction of 2^2m idempotents, dividing the discrete Clifford algebra in 2^2m subalgebras of dimension (k+m-1,k) - (k+m-3, k)

The large N limit of C/Z_N and supergravity

The C/Z_N orbifold of type II string theory has localized tachyons with m^2 ranging from -1+1/N to -2/N in units of 2/\alpha'. We show that by restricting attention to the lightest tachyons it is possible to take a zero-slope limit where N is taken to infinity while N\alpha' is held fixed. This is done by applying Buscher duality in the angular direction of the cone to obtain a supergravity solution on which the tachyons are gravitational instabilities. In this picture, supergravity provides a natural off-shell description of the tachyonic interactions. For example, the three-point couplings can be read off easily (to leading order in 1/N) from the supergravity action, and are in agreement with the on-shell couplings computed using CFT techniques.Comment: 17 pages, 1 figure; v2: reference adde

The Tachyon Potential in Witten's Superstring Field Theory

We study the tachyon potential in the NS sector of Witten's cubic superstring field theory. In this theory, the pure tachyon contribution to the potential has no minimum. We find that this remains the case when higher modes up to level two are included.Comment: Latex, 10 pages, 1 figure, published version, comments added regarding the absence of the twist-invariance and the singular behaviour of the potentia

Microstate solutions from black hole deconstruction

We present a new family of asymptotic AdS_3 x S^2 solutions to eleven dimensional supergravity compactified on a Calabi-Yau threefold. They originate from the backreaction of S^2-wrapped M2-branes, which play a central role in the deconstruction proposal for the microscopic interpretation of the D4-D0 black hole entropy. We show that they are free of possible pathologies such as closed timelike curves and discuss their holographic interpretation.Comment: 28 pages + appendice