57 research outputs found
From the Hitchin section to opers through nonabelian Hodge
For a complex simple simply connected Lie group , and a compact Riemann surface , we consider two sorts of families of flat -connections over . Each family is determined by a point of the base of Hitchin's integrable system for . One family consists of -opers, and depends on . The other family is built from solutions of Hitchin's equations, and depends on . We show that in the scaling limit , , we have . This establishes and generalizes a conjecture formulated by Gaiotto
Argyres-Seiberg duality and the Higgs branch
We demonstrate the agreement between the Higgs branches of two N=2 theories
proposed by Argyres and Seiberg to be S-dual, namely the SU(3) gauge theory
with six quarks, and the SU(2) gauge theory with one pair of quarks coupled to
the superconformal theory with E_6 flavor symmetry. In mathematical terms, we
demonstrate the equivalence between a hyperkaehler quotient of a linear space
and another hyperkaehler quotient involving the minimal nilpotent orbit of E_6,
modulo the identification of the twistor lines.Comment: 27 pages; v2: published versio
Matrix Models and D-branes in Twistor String Theory
We construct two matrix models from twistor string theory: one by dimensional
reduction onto a rational curve and another one by introducing noncommutative
coordinates on the fibres of the supertwistor space P^(3|4)->CP^1. We comment
on the interpretation of our matrix models in terms of topological D-branes and
relate them to a recently proposed string field theory. By extending one of the
models, we can carry over all the ingredients of the super ADHM construction to
a D-brane configuration in the supertwistor space P^(3|4). Eventually, we
present the analogue picture for the (super) Nahm construction.Comment: 1+37 pages, reference added, JHEP style, published versio
Asymptotic Spectroscopy of Rotating Black Holes
We calculate analytically the transmission and reflection amplitudes for
waves incident on a rotating black hole in d=4, analytically continued to
asymptotically large, nearly imaginary frequency. These amplitudes determine
the asymptotic resonant frequencies of the black hole, including quasinormal
modes, total-transmission modes and total-reflection modes. We identify these
modes with semiclassical bound states of a one-dimensional Schrodinger
equation, localized along contours in the complexified r-plane which connect
turning points of corresponding null geodesics. Each family of modes has a
characteristic temperature and chemical potential. The relations between them
provide hints about the microscopic description of the black hole in this
asymptotic regime.Comment: References adde
Perturbative Calculation of Quasinormal Modes of --Dimensional Black Holes
We study analytically quasinormal modes in a wide variety of black hole
spacetimes, including --dimensional asymptotically flat spacetimes and
non-asymptotically flat spacetimes (particular attention has been paid to the
four dimensional case). We extend the analytical calculation to include
first-order corrections to analytical expressions for quasinormal mode
frequencies by making use of a monodromy technique. All possible type
perturbations are included in this paper. The calculation performed in this
paper show that systematic expansions for uncharged black holes include
different corrections with the ones for charged black holes. This difference
makes them have a different --dependence relation in the first-order
correction formulae. The method applied above in calculating the first-order
corrections of quasinormal mode frequencies seems to be unavailable for black
holes with small charge. This result supports the Neitzke's prediction. On what
concerns quantum gravity we confirm the view that the in
Schwarzschild seems to be nothing but some numerical coincidences.Comment: 49 pages, 5 figure
On Minimal N=4 Topological Strings And The (1,k) Minimal Bosonic String
In this paper we consider tree-level scattering in the minimal N=4
topological string and show that a large class of N-point functions can be
recast in terms of corresponding amplitudes in the (1,k) minimal bosonic
string. This suggests a non-trivial relation between the minimal N=4
topological strings, the (1,k) minimal bosonic strings and their corresponding
ADE matrix models. This relation has interesting and far-reaching implications
for the topological sector of six-dimensional Little String Theories.Comment: lanlmac, 30 pages; v3 minor revisions, version published in JHE
Wilson Loops, Geometric Transitions and Bubbling Calabi-Yau's
Motivated by recent developments in the AdS/CFT correspondence, we provide
several alternative bulk descriptions of an arbitrary Wilson loop operator in
Chern-Simons theory. Wilson loop operators in Chern-Simons theory can be given
a description in terms of a configuration of branes or alternatively
anti-branes in the resolved conifold geometry. The representation of the Wilson
loop is encoded in the holonomy of the gauge field living on the dual brane
configuration. By letting the branes undergo a new type of geometric
transition, we argue that each Wilson loop operator can also be described by a
bubbling Calabi-Yau geometry, whose topology encodes the representation of the
Wilson loop. These Calabi-Yau manifolds provide a novel representation of knot
invariants. For the unknot we confirm these identifications to all orders in
the genus expansion.Comment: 26 pages; v.2 typos corrected, explanations clarified; v.3 typos
corrected, reference adde
Twistor Strings with Flavour
We explore the tree-level description of a class of N=2 UV-finite SYM
theories with fundamental flavour within a topological B-model twistor string
framework. In particular, we identify the twistor dual of the Sp(N) gauge
theory with one antisymmetric and four fundamental hypermultiplets, as well as
that of the SU(N) theory with 2N hypermultiplets. This is achieved by suitably
orientifolding/orbifolding the original N=4 setup of Witten and adding a
certain number of new topological 'flavour'-branes at the orientifold/orbifold
fixed planes to provide the fundamental matter. We further comment on the
appearance of these objects in the B-model on CP(3|4). An interesting aspect of
our construction is that, unlike the IIB description of these theories in terms
of D3 and D7-branes, on the twistor side part of the global flavour symmetry is
realised geometrically. We provide evidence for this correspondence by
calculating and matching amplitudes on both sides.Comment: 38+12 pages; uses axodraw.sty. v2: References added, minor
clarification
Ghost D-branes
We define a ghost D-brane in superstring theories as an object that cancels
the effects of an ordinary D-brane. The supergroups U(N|M) and OSp(N|M) arise
as gauge symmetries in the supersymmetric world-volume theory of D-branes and
ghost D-branes. A system with a pair of D-brane and ghost D-brane located at
the same location is physically equivalent to the closed string vacuum. When
they are separated, the system becomes a new brane configuration. We generalize
the type I/heterotic duality by including n ghost D9-branes on the type I side
and by considering the heterotic string whose gauge group is OSp(32+2n|2n).
Motivated by the type IIB S-duality applied to D9- and ghost D9-branes, we also
find type II-like closed superstrings with U(n|n) gauge symmetry.Comment: 49 pages, 6 figures, harvmac. v2: references and acknowledgements
adde
T-systems and Y-systems in integrable systems
The T and Y-systems are ubiquitous structures in classical and quantum
integrable systems. They are difference equations having a variety of aspects
related to commuting transfer matrices in solvable lattice models, q-characters
of Kirillov-Reshetikhin modules of quantum affine algebras, cluster algebras
with coefficients, periodicity conjectures of Zamolodchikov and others,
dilogarithm identities in conformal field theory, difference analogue of
L-operators in KP hierarchy, Stokes phenomena in 1d Schr\"odinger problem,
AdS/CFT correspondence, Toda field equations on discrete space-time, Laplace
sequence in discrete geometry, Fermionic character formulas and combinatorial
completeness of Bethe ansatz, Q-system and ideal gas with exclusion statistics,
analytic and thermodynamic Bethe ans\"atze, quantum transfer matrix method and
so forth. This review article is a collection of short reviews on these topics
which can be read more or less independently.Comment: 156 pages. Minor corrections including the last paragraph of sec.3.5,
eqs.(4.1), (5.28), (9.37) and (13.54). The published version (JPA topical
review) also needs these correction
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