Probing AdS4/CFT3 proposals beyond chiral rings

We calculate the superconformal Witten index for the Chern-Simons-matter theory which was proposed to describe multiple M2-branes on $C^2 X C^2/Z_k$. We consider a variant of this model, which exhibits explicit N=3 supersymmetry and has the advantage of not having an exotic branch of the moduli space. At $k=1$, we compare the index with that from the proposed gravity dual and find a disagreement.Comment: references added; introduction modifie

Quantum W-symmetry in AdS_3

It has recently been argued that, classically, massless higher spin theories in AdS_3 have an enlarged W_N-symmetry as the algebra of asymptotic isometries. In this note we provide evidence that this symmetry is realised (perturbatively) in the quantum theory. We perform a one loop computation of the fluctuations for a massless spin $s$ field around a thermal AdS_3 background. The resulting determinants are evaluated using the heat kernel techniques of arXiv:0911.5085. The answer factorises holomorphically, and the contributions from the various spin $s$ fields organise themselves into vacuum characters of the W_N symmetry. For the case of the hs(1,1) theory consisting of an infinite tower of massless higher spin particles, the resulting answer can be simply expressed in terms of (two copies of) the MacMahon function.Comment: 23 pages; v2: References adde

Supersymmetric Chern-Simons Theories with Vector Matter

In this paper we discuss SU(N) Chern-Simons theories at level k with both fermionic and bosonic vector matter. In particular we present an exact calculation of the free energy of the N=2 supersymmetric model (with one chiral field) for all values of the 't Hooft coupling in the large N limit. This is done by using a generalization of the standard Hubbard-Stratanovich method because the SUSY model contains higher order polynomial interactions.Comment: 46 pages, 24 figures, v2: comments and references added, v3: a footnote in Section 3.5 adde

Supersymmetry Breaking in Chern-Simons-matter Theories

Some of supersymmetric Chern-Simons theories are known to exhibit supersymmetry breaking when the Chern-Simons level is less than a certain number. The mechanism of the supersymmetry breaking is, however, not clear from the field theory viewpoint. In this paper, we discuss vacuum states of ${\cal N}=2$ pure Chern-Simons theory and ${\cal N}=2$ Chern-Simons-matter theories of quiver type using related theories in which Chern-Simons terms are replaced with (anti-)fundamental chiral multiplets. In the latter theories, supersymmetry breaking can be shown to occur by examining that the vacuum energy is non-zero.Comment: 17 pages, 3 figures, v2) references adde

On thermodynamics of N=6 superconformal Chern-Simons theory

We study thermodynamics of N=6 superconformal Chern-Simons theory by computing quantum corrections to the free energy. We find that in weakly coupled ABJM theory on R(2) x S(1), the leading correction is non-analytic in the 't Hooft coupling lambda, and is approximately of order lambda^2 log(lambda)^3. The free energy is expressed in terms of the scalar thermal mass m, which is generated by screening effects. We show that this mass vanishes to 1-loop order. We then go on to 2-loop order where we find a finite and positive mass squared m^2. We discuss differences in the calculation between Coulomb and Lorentz gauge. Our results indicate that the free energy is a monotonic function in lambda which interpolates smoothly to the N^(3/2) behaviour at strong coupling.Comment: 29 pages. v2: references added. v3: minor changes, references added, published versio

Higher Spin Gauge Theory and Holography: The Three-Point Functions

In this paper we calculate the tree level three-point functions of Vasiliev's higher spin gauge theory in AdS4 and find agreement with the correlators of the free field theory of N massless scalars in three dimensions in the O(N) singlet sector. This provides substantial evidence that Vasiliev theory is dual to the free field theory, thus verifying a conjecture of Klebanov and Polyakov. We also find agreement with the critical O(N) vector model, when the bulk scalar field is subject to the alternative boundary condition such that its dual operator has classical dimension 2.Comment: 90 pages, 5 figures; v4, minor changes in the introductio

On the worldsheet theory of the type IIA AdS(4) x CP(3) superstring

We perform a detailed study of the type IIA superstring in AdS(4) x CP(3). After introducing suitable bosonic light-cone and fermionic kappa worldsheet gauges we derive the pure boson and fermion SU(2|2) x U(1) covariant light-cone Hamiltonian up to quartic order in fields. As a first application of our derivation we calculate energy shifts for string configurations in a closed fermionic subsector and successfully match these with a set of light-cone Bethe equations. We then turn to investigate the mismatch between the degrees of freedom of scattering states and oscillatory string modes. Since only light string modes appear as fundamental Bethe roots in the scattering theory, the physical role of the remaining $4_F+4_B$ massive oscillators is rather unclear. By continuing a line of research initiated by Zarembo, we shed light on this question by calculating quantum corrections for the propagators of the bosonic massive fields. We show that, once loop corrections are incorporated, the massive coordinates dissolve in a continuum state of two light particles.Comment: 40 pages, 2 figures. v3: Minor clarifications made and reference list updated. Published version

Electroweak Symmetry Breaking in the DSSM

We study the theoretical and phenomenological consequences of modifying the Kahler potential of the MSSM two Higgs doublet sector. Such modifications naturally arise when the Higgs sector mixes with a quasi-hidden conformal sector, as in some F-theory GUT models. In the Delta-deformed Supersymmetric Standard Model (DSSM), the Higgs fields are operators with non-trivial scaling dimension 1 < Delta < 2. The Kahler metric is singular at the origin of field space due to the presence of quasi-hidden sector states which get their mass from the Higgs vevs. The presence of these extra states leads to the fact that even as Delta approaches 1, the DSSM does not reduce to the MSSM. In particular, the Higgs can naturally be heavier than the W- and Z-bosons. Perturbative gauge coupling unification, a large top quark Yukawa, and consistency with precision electroweak can all be maintained for Delta close to unity. Moreover, such values of Delta can naturally be obtained in string-motivated constructions. The quasi-hidden sector generically contains states charged under SU(5)_GUT as well as gauge singlets, leading to a rich, albeit model-dependent, collider phenomenology.Comment: v3: 40 pages, 3 figures, references added, typos correcte

d=3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories

We study three dimensional O(N)_k and U(N)_k Chern-Simons theories coupled to a scalar field in the fundamental representation, in the large N limit. For infinite k this is just the singlet sector of the O(N) (U(N)) vector model, which is conjectured to be dual to Vasiliev's higher spin gravity theory on AdS_4. For large k and N we obtain a parity-breaking deformation of this theory, controlled by the 't Hooft coupling lambda = 4 \pi N / k. For infinite N we argue (and show explicitly at two-loop order) that the theories with finite lambda are conformally invariant, and also have an exactly marginal (\phi^2)^3 deformation. For large but finite N and small 't Hooft coupling lambda, we show that there is still a line of fixed points parameterized by the 't Hooft coupling lambda. We show that, at infinite N, the interacting non-parity-invariant theory with finite lambda has the same spectrum of primary operators as the free theory, consisting of an infinite tower of conserved higher-spin currents and a scalar operator with scaling dimension \Delta=1; however, the correlation functions of these operators do depend on lambda. Our results suggest that there should exist a family of higher spin gravity theories, parameterized by lambda, and continuously connected to Vasiliev's theory. For finite N the higher spin currents are not conserved.Comment: 34 pages, 29 figures. v2: added reference

Entanglement Entropy of 3-d Conformal Gauge Theories with Many Flavors

Three-dimensional conformal field theories (CFTs) of deconfined gauge fields coupled to gapless flavors of fermionic and bosonic matter describe quantum critical points of condensed matter systems in two spatial dimensions. An important characteristic of these CFTs is the finite part of the entanglement entropy across a circle. The negative of this quantity is equal to the finite part of the free energy of the Euclidean CFT on the three-sphere, and it has been proposed to satisfy the so called F-theorem, which states that it decreases under RG flow and is stationary at RG fixed points. We calculate the three-sphere free energy of non-supersymmetric gauge theory with a large number N_F of bosonic and/or fermionic flavors to the first subleading order in 1/N_F. We also calculate the exact free energies of the analogous chiral and non-chiral {\cal N} = 2 supersymmetric theories using localization, and find agreement with the 1/N_F expansion. We analyze some RG flows of supersymmetric theories, providing further evidence for the F-theorem.Comment: 31 pages, 2 figures; v2 refs added, minor change