176 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
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
Gravity in the 3+1-Split Formalism II: Self-Duality and the Emergence of the Gravitational Chern-Simons in the Boundary
We study self-duality in the context of the 3+1-split formalism of gravity
with non-zero cosmological constant. Lorentzian self-dual configurations are
conformally flat spacetimes and have boundary data determined by classical
solutions of the three-dimensional gravitational Chern-Simons. For Euclidean
self-dual configurations, the relationship between their boundary initial
positions and initial velocity is also determined by the three-dimensional
gravitational Chern-Simons. Our results imply that bulk self-dual
configurations are holographically described by the gravitational Chern-Simons
theory which can either viewed as a boundary generating functional or as a
boundary effective action.Comment: 25 pages; v2: minor improvements, references adde
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
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
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
Exact ABJM Partition Function from TBA
We report on the exact computation of the S^3 partition function of
U(N)_k\times U(N)_{-k} ABJM theory for k=1, N=1,...,19. The result is a
polynomial in \pi^{-1} with rational coefficients. As an application of our
results we numerically determine the coefficient of the membrane 1-instanton
correction to the partition function.Comment: 8 pages, 2 figures. v3: introduction expanded, section about
numerical applications adde
On renormalization group flows and the a-theorem in 6d
We study the extension of the approach to the a-theorem of Komargodski and
Schwimmer to quantum field theories in d=6 spacetime dimensions. The dilaton
effective action is obtained up to 6th order in derivatives. The anomaly flow
a_UV - a_IR is the coefficient of the 6-derivative Euler anomaly term in this
action. It then appears at order p^6 in the low energy limit of n-point
scattering amplitudes of the dilaton for n > 3. The detailed structure with the
correct anomaly coefficient is confirmed by direct calculation in two examples:
(i) the case of explicitly broken conformal symmetry is illustrated by the free
massive scalar field, and (ii) the case of spontaneously broken conformal
symmetry is demonstrated by the (2,0) theory on the Coulomb branch. In the
latter example, the dilaton is a dynamical field so 4-derivative terms in the
action also affect n-point amplitudes at order p^6. The calculation in the
(2,0) theory is done by analyzing an M5-brane probe in AdS_7 x S^4.
Given the confirmation in two distinct models, we attempt to use dispersion
relations to prove that the anomaly flow is positive in general. Unfortunately
the 4-point matrix element of the Euler anomaly is proportional to stu and
vanishes for forward scattering. Thus the optical theorem cannot be applied to
show positivity. Instead the anomaly flow is given by a dispersion sum rule in
which the integrand does not have definite sign. It may be possible to base a
proof of the a-theorem on the analyticity and unitarity properties of the
6-point function, but our preliminary study reveals some difficulties.Comment: 41 pages, 5 figure
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