57 research outputs found
Comments on F-maximization and R-symmetry in 3D SCFTs
We report preliminary results on the recently proposed F-maximization
principle in 3D SCFTs. We compute numerically in the large-N limit the free
energy on the three-sphere of an N=2 Chern-Simons-Matter theory with a single
adjoint chiral superfield which is known to exhibit a pattern of accidental
symmetries associated to chiral superfields that hit the unitarity bound and
become free. We observe that the F-maximization principle produces a U(1)
R-symmetry consistent with previously obtained bounds but inconsistent with a
postulated Seiberg-like duality. Potential modifications of the principle
associated to the decoupling fields do not appear to be sufficient to account
for the observed violations.Comment: 17 pages, 3 figures; v2 a reference has been added, a missing factor
of 2 has been corrected in eq (3.3) and the numerical results have been
accordingly updated. The new results do not show any obvious signs of
violation of previously obtained bounds. A potential disagreement with a
postulated Seiberg-like duality is note
ABJM theory as a Fermi gas
The partition function on the three-sphere of many supersymmetric
Chern-Simons-matter theories reduces, by localization, to a matrix model. We
develop a new method to study these models in the M-theory limit, but at all
orders in the 1/N expansion. The method is based on reformulating the matrix
model as the partition function of an ideal Fermi gas with a non-trivial,
one-particle quantum Hamiltonian. This new approach leads to a completely
elementary derivation of the N^{3/2} behavior for ABJM theory and N=3 quiver
Chern-Simons-matter theories. In addition, the full series of 1/N corrections
to the original matrix integral can be simply determined by a next-to-leading
calculation in the WKB or semiclassical expansion of the quantum gas, and we
show that, for several quiver Chern-Simons-matter theories, it is given by an
Airy function. This generalizes a recent result of Fuji, Hirano and Moriyama
for ABJM theory. It turns out that the semiclassical expansion of the Fermi gas
corresponds to a strong coupling expansion in type IIA theory, and it is dual
to the genus expansion. This allows us to calculate explicitly non-perturbative
effects due to D2-brane instantons in the AdS background.Comment: 52 pages, 11 figures. v3: references, corrections and clarifications
added, plus a footnote on the relation to the recent work by Hanada et a
Perturbing gauge/gravity duals by a Romans mass
We show how to produce algorithmically gravity solutions in massive IIA (as
infinitesimal first order perturbations in the Romans mass parameter) dual to
assigned conformal field theories. We illustrate the procedure on a family of
Chern--Simons--matter conformal field theories that we recently obtained from
the N=6 theory by waiving the condition that the levels sum up to zero.Comment: 30 page
N=2 solutions of massive type IIA and their Chern-Simons duals
We find explicit AdS4 solutions of massive type IIA with N=2 supersymmetry
obtained deforming with a Roman mass the type IIA supersymmetric reduction of
the M theory background AdS4 times M111. The family of solutions have SU(3)
times SU(3) structure and isometry SU(3) times U(1)^2. They are conjectured to
be dual to three-dimensional N=2 Chern-Simons theories with generic
Chern-Simons couplings and gauge group ranks.Comment: 20 pages, 1 figure, comments and references adde
Massive type IIA string theory cannot be strongly coupled
Understanding the strong coupling limit of massive type IIA string theory is
a longstanding problem. We argue that perhaps this problem does not exist;
namely, there may be no strongly coupled solutions of the massive theory. We
show explicitly that massive type IIA string theory can never be strongly
coupled in a weakly curved region of space-time. We illustrate our general
claim with two classes of massive solutions in AdS4xCP3: one, previously known,
with N = 1 supersymmetry, and a new one with N = 2 supersymmetry. Both
solutions are dual to d = 3 Chern-Simons-matter theories. In both these massive
examples, as the rank N of the gauge group is increased, the dilaton initially
increases in the same way as in the corresponding massless case; before it can
reach the M-theory regime, however, it enters a second regime, in which the
dilaton decreases even as N increases. In the N = 2 case, we find
supersymmetry-preserving gauge-invariant monopole operators whose mass is
independent of N. This predicts the existence of branes which stay light even
when the dilaton decreases. We show that, on the gravity side, these states
originate from D2-D0 bound states wrapping the vanishing two-cycle of a
conifold singularity that develops at large N.Comment: 43 pages, 5 figures. v2: added reference
The gauge dual of Romans mass
We deform the recently proposed holographic duality between the ABJM N=6
Chern-Simons-matter theory and type IIA string theory in AdS4xCP3. We add a
non-zero Romans mass F_0, whose dual we identify as the sum of the Chern-Simons
levels for the two gauge groups. One can naturally identify four different
theories, with different amounts of supersymmetry and of flavor symmetry.Comment: 26 pages. v4: Corrected the sign for the probe brane potentia
Supersymmetric States in Large N Chern-Simons-Matter Theories
In this paper we study the spectrum of BPS operators/states in N=2
superconformal U(N) Chern-Simons-matter theories with adjoint chiral matter
fields, with and without superpotential. The superconformal indices and
conjectures on the full supersymmetric spectrum of the theories in the large N
limit with up to two adjoint matter fields are presented. Our results suggest
that some of these theories may have supergravity duals at strong coupling,
while some others may be dual to higher spin theories of gravity at strong
coupling. For the N=2 theory with no superpotential, we study the
renormalization of R-charge at finite 't Hooft coupling using "Z-minimization".
A particularly intriguing result is found in the case of one adjoint matter.Comment: 53 pages, 18 figures. v2: improved numerics, additional comments
adde
A note on the holography of Chern-Simons matter theories with flavour
We study a three-dimensional N=3 U(N)_k x U(N)_{-k} Chern-Simons matter
theory with flavour, corresponding to the N=6
Aharony-Bergman-Jafferis-Maldacena CSM theory coupled to 2N_f fundamental
fields. The dual holographic description is given by the near-horizon geometry
of N M2-branes at a particular hypertoric geometry M_8. We explicitly construct
the space M_8 and match its isometries to the global symmetries of the field
theory. We also discuss the model in the quenched approximation by embedding
probe D6-branes in AdS_4 x CP^3.Comment: 21 pages, 3 figures, references added, minor changes (in particular
Fig. 2
Towards the F-Theorem: N=2 Field Theories on the Three-Sphere
For 3-dimensional field theories with {\cal N}=2 supersymmetry the Euclidean
path integrals on the three-sphere can be calculated using the method of
localization; they reduce to certain matrix integrals that depend on the
R-charges of the matter fields. We solve a number of such large N matrix models
and calculate the free energy F as a function of the trial R-charges consistent
with the marginality of the superpotential. In all our {\cal N}=2
superconformal examples, the local maximization of F yields answers that scale
as N^{3/2} and agree with the dual M-theory backgrounds AdS_4 x Y, where Y are
7-dimensional Sasaki-Einstein spaces. We also find in toric examples that local
F-maximization is equivalent to the minimization of the volume of Y over the
space of Sasakian metrics, a procedure also referred to as Z-minimization.
Moreover, we find that the functions F and Z are related for any trial
R-charges. In the models we study F is positive and decreases along RG flows.
We therefore propose the "F-theorem" that we hope applies to all 3-d field
theories: the finite part of the free energy on the three-sphere decreases
along RG trajectories and is stationary at RG fixed points. We also show that
in an infinite class of Chern-Simons-matter gauge theories where the
Chern-Simons levels do not sum to zero, the free energy grows as N^{5/3} at
large N. This non-trivial scaling matches that of the free energy of the
gravity duals in type IIA string theory with Romans mass.Comment: 66 pages, 10 figures; v2: refs. added, minor improvement
Refined Checks and Exact Dualities in Three Dimensions
We discuss and provide nontrivial evidence for a large class of dualities in
three-dimensional field theories with different gauge groups. We match the full
partition functions of the dual phases for any value of the couplings to
underpin our proposals. We focus on two classes of models. The first class,
motivated by the AdS/CFT conjecture, consists of necklace U(N) quiver gauge
theories with non chiral matter fields. We also consider orientifold
projections and establish dualities among necklace quivers with alternating
orthogonal and symplectic groups. The second class consists of theories with
tensor matter fields with free theory duals. In most of these cases the
R-symmetry mixes with IR accidental symmetries and we develop the prescription
to include their contribution into the partition function and the extremization
problem accordingly.Comment: 38 pages, 3 figure, using jheppu
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