425 research outputs found
BPS partition functions in N = 4 Yang-Mills theory on T^4
We consider N = 4 Yang-Mills theory on a flat four-torus with the R-symmetry
current coupled to a flat background connection. The partition function depends
on the coupling constant of the theory, but when it is expanded in a power
series in the R-symmetry connection around the loci at which one of the
supersymmetries is unbroken, the constant and linear terms are in fact
independent of the coupling constant and can be computed at weak coupling for
all non-trivial 't Hooft fluxes. The case of a trivial 't Hooft flux is
difficult because of infrared problems, but the corresponding terms in the
partition function are uniquely determined by S-duality.Comment: 23 pages, v2 Minor correction
Janus Configurations, Chern-Simons Couplings, And The Theta-Angle in N=4 Super Yang-Mills Theory
We generalize the half-BPS Janus configuration of four-dimensional N=4 super
Yang-Mills theory to allow the theta-angle, as well as the gauge coupling, to
vary with position. We show that the existence of this generalization is
closely related to the existence of novel three-dimensional Chern-Simons
theories with N=4 supersymmetry. Another closely related problem, which we also
elucidate, is the D3-NS5 system in the presence of a four-dimensional
theta-angle.Comment: 66 p
Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
We use localization techniques to compute the expectation values of
supersymmetric Wilson loops in Chern-Simons theories with matter. We find the
path-integral reduces to a non-Gaussian matrix model. The Wilson loops we
consider preserve a single complex supersymmetry, and exist in any N=2 theory,
though the localization requires superconformal symmetry. We present explicit
results for the cases of pure Chern-Simons theory with gauge group U(N),
showing agreement with the known results, and ABJM, showing agreement with
perturbative calculations. Our method applies to other theories, such as
Gaiotto-Witten theories, BLG, and their variants.Comment: 32 page
N=4 Superconformal Algebra and the Entropy of HyperKahler Manifolds
We study the elliptic genera of hyperKahler manifolds using the
representation theory of N=4 superconformal algebra. We consider the
decomposition of the elliptic genera in terms of N=4 irreducible characters,
and derive the rate of increase of the multiplicities of half-BPS
representations making use of Rademacher expansion. Exponential increase of the
multiplicity suggests that we can associate the notion of an entropy to the
geometry of hyperKahler manifolds. In the case of symmetric products of K3
surfaces our entropy agrees with the black hole entropy of D5-D1 system.Comment: 25 pages, 1 figur
D-brane Charges in Gravitational Duals of 2+1 Dimensional Gauge Theories and Duality Cascades
We perform a systematic analysis of the D-brane charges associated with
string theory realizations of d=3 gauge theories, focusing on the examples of
the N=4 supersymmetric U(N)xU(N+M) Yang-Mills theory and the N=3 supersymmetric
U(N)xU(N+M) Yang-Mills-Chern-Simons theory. We use both the brane construction
of these theories and their dual string theory backgrounds in the supergravity
approximation. In the N=4 case we generalize the previously known gravitational
duals to arbitrary values of the gauge couplings, and present a precise mapping
between the gravity and field theory parameters. In the N=3 case, which (for
some values of N and M) flows to an N=6 supersymmetric Chern-Simons-matter
theory in the IR, we argue that the careful analysis of the charges leads to a
shift in the value of the B-field in the IR solution by 1/2, in units where its
periodicity is one, compared to previous claims. We also suggest that the N=3
theories may exhibit, for some values of N and M, duality cascades similar to
those of the Klebanov-Strassler theory.Comment: 47 pages, 9 figures; minor changes, references adde
D-brane anomaly inflow revisited
Axial and gravitational anomaly of field theories, when embedded in string
theory, must be accompanied by canceling inflow. We give a self-contained
overview for various world-volume theories, and clarify the role of smeared
magnetic sources in I-brane/D-brane cases. The proper anomaly descent of the
source, as demanded by regularity of RR field strengths H's, turns out to be an
essential ingredient. We show how this allows correct inflow to be generated
for all such theories, including self-dual cases, and also that the mechanism
is now insensitive to the choice between the two related but inequivalent forms
of D-brane Chern-Simons couplings. In particular, SO(6)_R axial anomaly of d=4
maximal SYM is canceled by the inflow onto D3-branes via the standard minimal
coupling to C_4. We also propose how, for the anomaly cancelation, the four
types of Orientifold planes should be coupled to the spacetime curvatures, of
which conflicting claims existed previously.Comment: 41 pages, references updated; version to appear in JHE
Orientifolds and the Refined Topological String
We study refined topological string theory in the presence of orientifolds by
counting second-quantized BPS states in M-theory. This leads us to propose a
new integrality condition for both refined and unrefined topological strings
when orientifolds are present. We define the SO(2N) refined Chern-Simons theory
which computes refined open string amplitudes for branes wrapping Seifert
three-manifolds. We use the SO(2N) refined Chern-Simons theory to compute new
invariants of torus knots that generalize the Kauffman polynomials. At large N,
the SO(2N) refined Chern-Simons theory on the three-sphere is dual to refined
topological strings on an orientifold of the resolved conifold, generalizing
the Gopakumar-Sinha-Vafa duality. Finally, we use the (2,0) theory to define
and solve refined Chern-Simons theory for all ADE gauge groups
Super-A-polynomials for Twist Knots
We conjecture formulae of the colored superpolynomials for a class of twist
knots where p denotes the number of full twists. The validity of the
formulae is checked by applying differentials and taking special limits. Using
the formulae, we compute both the classical and quantum super-A-polynomial for
the twist knots with small values of p. The results support the categorified
versions of the generalized volume conjecture and the quantum volume
conjecture. Furthermore, we obtain the evidence that the Q-deformed
A-polynomials can be identified with the augmentation polynomials of knot
contact homology in the case of the twist knots.Comment: 22+16 pages, 16 tables and 5 figures; with a Maple program by Xinyu
Sun and a Mathematica notebook in the ancillary files linked on the right; v2
change in appendix B, typos corrected and references added; v3 change in
section 3.3; v4 corrections in Ooguri-Vafa polynomials and quantum
super-A-polynomials for 7_2 and 8_1 are adde
A Terminal Velocity on the Landscape: Particle Production near Extra Species Loci in Higher Dimensions
We investigate particle production near extra species loci (ESL) in a higher
dimensional field space and derive a speed limit in moduli space at weak
coupling. This terminal velocity is set by the characteristic ESL-separation
and the coupling of the extra degrees of freedom to the moduli, but it is
independent of the moduli's potential if the dimensionality of the field space
is considerably larger than the dimensionality of the loci, D >> d. Once the
terminal velocity is approached, particles are produced at a plethora of nearby
ESLs, preventing a further increase in speed via their backreaction. It is
possible to drive inflation at the terminal velocity, providing a
generalization of trapped inflation with attractive features: we find that more
than sixty e-folds of inflation for sub-Planckian excursions in field space are
possible if ESLs are ubiquitous, without fine tuning of initial conditions and
less tuned potentials. We construct a simple, observationally viable model with
a slightly red scalar power-spectrum and suppressed gravitational waves; we
comment on the presence of additional observational signatures originating from
IR-cascading and individual massive particles. We also show that
moduli-trapping at an ESL is suppressed for D >> d, hindering dynamical
selection of high-symmetry vacua on the landscape based on this mechanism.Comment: 46 pages, 6 figures. V3: typos corrected compared to JHEP version,
conclusions unchange
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