1,179 research outputs found
Quantization via Mirror Symmetry
When combined with mirror symmetry, the A-model approach to quantization
leads to a fairly simple and tractable problem. The most interesting part of
the problem then becomes finding the mirror of the coisotropic brane. We
illustrate how it can be addressed in a number of interesting examples related
to representation theory and gauge theory, in which mirror geometry is
naturally associated with the Langlands dual group. Hyperholomorphic sheaves
and (B,B,B) branes play an important role in the B-model approach to
quantization.Comment: 44 p
Counting RG flows
Interpreting renormalization group flows as solitons interpolating between
different fixed points, we ask various questions that are normally asked in
soliton physics but not in renormalization theory. Can one count RG flows? Are
there different "topological sectors" for RG flows? What is the moduli space of
an RG flow, and how does it compare to familiar moduli spaces of
(supersymmetric) dowain walls? Analyzing these questions in a wide variety of
contexts --- from counting RG walls to AdS/CFT correspondence --- will not only
provide favorable answers, but will also lead us to a unified general framework
that is powerful enough to account for peculiar RG flows and predict new
physical phenomena. Namely, using Bott's version of Morse theory we relate the
topology of conformal manifolds to certain properties of RG flows that can be
used as precise diagnostics and "topological obstructions" for the strong form
of the C-theorem in any dimension. Moreover, this framework suggests a precise
mechanism for how the violation of the strong C-theorem happens and predicts
"phase transitions" along the RG flow when the topological obstruction is
non-trivial. Along the way, we also find new conformal manifolds in well-known
4d CFT's and point out connections with the superconformal index and
classifying spaces of global symmetry groups.Comment: 39 pages. Please, send me examples of peculiar RG flows, especially
the ones which do not appear to be (ac)counted in this framewor
Supersymmetric Spin Glass
The evidently supersymmetric four-dimensional Wess-Zumino model with quenched
disorder is considered at the one-loop level. The infrared fixed points of a
beta-function form the moduli space where two types of phases were
found: with and without replica symmetry. While the former phase possesses only
a trivial fixed point, this point become unstable in the latter phase which may
be interpreted as a spin glass phase.Comment: latex, 8 pages, 2 Postscript figure
Trisecting non-Lagrangian theories
We propose a way to define and compute invariants of general smooth
4-manifolds based on topological twists of non-Lagrangian 4d N=2 and N=3
theories in which the problem is reduced to a fairly standard computation in
topological A-model, albeit with rather unusual targets, such as compact and
non-compact Gepner models, asymmetric orbifolds, N=(2,2) linear dilaton
theories, "self-mirror" geometries, varieties with complex multiplication, etc.Comment: 49 pages, 8 figures, 8 tables, v2: a reference adde
K-Theory, Reality, and Orientifolds
We use equivariant K-theory to classify charges of new (possibly
non-supersymmetric) states localized on various orientifolds in Type II string
theory. We also comment on the stringy construction of new D-branes and
demonstrate the discrete electric-magnetic duality in Type I brane systems with
p+q=7, as proposed by Witten.Comment: 26 pages, harvmac, no figure
Exceptional knot homology
The goal of this article is twofold. First, we find a natural home for the
double affine Hecke algebras (DAHA) in the physics of BPS states. Second, we
introduce new invariants of torus knots and links called "hyperpolynomials"
that address the "problem of negative coefficients" often encountered in
DAHA-based approaches to homological invariants of torus knots and links.
Furthermore, from the physics of BPS states and the spectra of singularities
associated with Landau-Ginzburg potentials, we also describe a rich structure
of differentials that act on homological knot invariants for exceptional groups
and uniquely determine the latter for torus knots.Comment: 44 pages, 4 figure
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