522 research outputs found
Lectures on mathematical aspects of (twisted) supersymmetric gauge theories
Supersymmetric gauge theories have played a central role in applications of
quantum field theory to mathematics. Topologically twisted supersymmetric gauge
theories often admit a rigorous mathematical description: for example, the
Donaldson invariants of a 4-manifold can be interpreted as the correlation
functions of a topologically twisted N=2 gauge theory. The aim of these
lectures is to describe a mathematical formulation of partially-twisted
supersymmetric gauge theories (in perturbation theory). These partially twisted
theories are intermediate in complexity between the physical theory and the
topologically twisted theories. Moreover, we will sketch how the operators of
such a theory form a two complex dimensional analog of a vertex algebra.
Finally, we will consider a deformation of the N=1 theory and discuss its
relation to the Yangian, as explained in arXiv:1308.0370 and arXiv:1303.2632.Comment: Notes from a lecture series by the first author at the Les Houches
Winter School on Mathematical Physics in 2012. To appear in the proceedings
of this conference. Related to papers arXiv:1308.0370, arXiv:1303.2632, and
arXiv:1111.423
Charge Lattices and Consistency of 6D Supergravity
We extend the known consistency conditions on the low-energy theory of
six-dimensional N = 1 supergravity. We review some facts about the theory of
two-form gauge fields and conclude that the charge lattice Gamma for such a
theory has to be self-dual. The Green-Schwarz anomaly cancellation conditions
in the supergravity theory determine a sublattice of Gamma. The condition that
this sublattice can be extended to a self-dual lattice Gamma leads to a strong
constraint on theories that otherwise appear to be self-consistent.Comment: 15 pages. v2: minor changes; references, additional example added;
v3: minor corrections and clarifications added, JHEP versio
Entropy of the self-dual string soliton
We compute the entropy and the corresponding central charge of the self-dual
string soliton in the supergravity regime using the blackfold description of
the fully localized M2-M5 intersection.Comment: 15 pages, 1 figure, harvma
On Flux Quantization in F-Theory II: Unitary and Symplectic Gauge Groups
We study the quantization of the M-theory G-flux on elliptically fibered
Calabi-Yau fourfolds with singularities giving rise to unitary and symplectic
gauge groups. We seek and find its relation to the Freed-Witten quantization of
worldvolume fluxes on 7-branes in type IIB orientifold compactifications on
Calabi-Yau threefolds. By explicitly constructing the appropriate four-cycles
on which to calculate the periods of the second Chern class of the fourfolds,
we find that there is a half-integral shift in the quantization of G-flux
whenever the corresponding dual 7-brane is wrapped on a non-spin submanifold.
This correspondence of quantizations holds for all unitary and symplectic gauge
groups, except for SU(3), which behaves mysteriously. We also perform our
analysis in the case where, in addition to the aforementioned gauge groups,
there is also a 'flavor' U(1)-gauge group.Comment: 33 pages, 4 figure
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
BPS black holes, the Hesse potential, and the topological string
The Hesse potential is constructed for a class of four-dimensional N=2
supersymmetric effective actions with S- and T-duality by performing the
relevant Legendre transform by iteration. It is a function of fields that
transform under duality according to an arithmetic subgroup of the classical
dualities reflecting the monodromies of the underlying string compactification.
These transformations are not subject to corrections, unlike the
transformations of the fields that appear in the effective action which are
affected by the presence of higher-derivative couplings. The class of actions
that are considered includes those of the FHSV and the STU model. We also
consider heterotic N=4 supersymmetric compactifications. The Hesse potential,
which is equal to the free energy function for BPS black holes, is manifestly
duality invariant. Generically it can be expanded in terms of powers of the
modulus that represents the inverse topological string coupling constant,
, and its complex conjugate. The terms depending holomorphically on
are expected to correspond to the topological string partition function and
this expectation is explicitly verified in two cases. Terms proportional to
mixed powers of and are in principle present.Comment: 28 pages, LaTeX, added comment
Mycobacterium avium-intracellulare cellulitis occurring with septic arthritis after joint injection: a case report
BACKGROUND: Cellulitis caused by Mycobacterium avium-intracellulare has rarely been described. Mycobacterium avium-intracellulare is a rare cause of septic arthritis after intra-articular injection, though the causative role of injection is difficult to ascertain in such cases. CASE PRESENTATION: A 57-year-old with rheumatoid arthritis treated with prednisone and azathioprine developed bilateral painful degenerative shoulder arthritis. After corticosteroid injections into both acromioclavicular joints, he developed bilateral cellulitis centered over the injection sites. Skin biopsy showed non-caseating granulomas, and culture grew Mycobacterium avium-intracellulare. Joint aspiration also revealed Mycobacterium avium-intracellulare infection. CONCLUSION: Although rare, skin and joint infections caused by Mycobacterium avium-intracellulare should be considered in any immunocompromised host, particularly after intra-articular injection. Stains for acid-fast bacilli may be negative in pathologic samples even in the presence of infection; cultures of tissue specimens should always be obtained
Gauge Fluxes in F-theory and Type IIB Orientifolds
We provide a detailed correspondence between G_4 gauge fluxes in F-theory
compactifications with SU(n) and SU(n)x(1) gauge symmetry and their Type IIB
orientifold limit. Based on the resolution of the relevant F-theory Tate models
we classify the factorisable G_4-fluxes and match them with the set of
universal D5-tadpole free U(1)-fluxes in Type IIB. Where available, the global
version of the universal spectral cover flux corresponds to Type IIB gauge flux
associated with a massive diagonal U(1). In U(1)-restricted Tate models extra
massless abelian fluxes exist which are associated with specific linear
combinations of Type IIB fluxes. Key to a quantitative match between F-theory
and Type IIB is a proper treatment of the conifold singularity encountered in
the Sen limit of generic F-theory models. We also shed further light on the
brane recombination process relating generic and U(1)-restricted Tate models.Comment: 53 pages, 3 figures; v2: Refs added; v3: minor corrections to match
version published in JHE
On Flux Quantization in F-Theory
We study the problem of four-form flux quantization in F-theory
compactifications. We prove that for smooth, elliptically fibered Calabi-Yau
fourfolds with a Weierstrass representation, the flux is always integrally
quantized. This implies that any possible half-integral quantization effects
must come from 7-branes, i.e. from singularities of the fourfold. We
subsequently analyze the quantization rule on explicit fourfolds with Sp(N)
singularities, and connect our findings via Sen's limit to IIB string theory.
Via direct computations we find that the four-form is half-integrally quantized
whenever the corresponding 7-brane stacks wrap non-spin complex surfaces, in
accordance with the perturbative Freed-Witten anomaly. Our calculations on the
fourfolds are done via toric techniques, whereas in IIB we rely on Sen's
tachyon condensation picture to treat bound states of branes. Finally, we give
general formulae for the curvature- and flux-induced D3 tadpoles for general
fourfolds with Sp(N) singularities.Comment: 46 page
BPS dyons and Hesse flow
We revisit BPS solutions to classical N=2 low energy effective gauge
theories. It is shown that the BPS equations can be solved in full generality
by the introduction of a Hesse potential, a symplectic analog of the
holomorphic prepotential. We explain how for non-spherically symmetric,
non-mutually local solutions, the notion of attractor flow generalizes to
gradient flow with respect to the Hesse potential. Furthermore we show that in
general there is a non-trivial magnetic complement to this flow equation that
is sourced by the momentum current in the solution.Comment: 25 pages, references adde
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