1,930 research outputs found

### Computation Of Some Zamolodchikov Volumes, With An Application

We compute the Zamolodchikov volumes of some moduli spaces of conformal field
theories with target spaces K3, T4, and their symmetric products. As an
application we argue that sequences of conformal field theories, built from
products of such symmetric products, almost never have a holographic dual with
weakly coupled gravity.Comment: 20 pages, 1 figur

### Four-dimensional N=2 Field Theory and Physical Mathematics

We give a summary of a talk delivered at the 2012 International Congress on
Mathematical Physics. We review d=4, N=2 quantum field theory and some of the
exact statements which can be made about it. We discuss the wall-crossing
phenomenon. An interesting application is a new construction of hyperkahler
metrics on certain manifolds. Then we discuss geometric constructions which
lead to exact results on the BPS spectra for some d=4, N=2 field theories and
on expectation values of -- for example -- Wilson line operators. These new
constructions have interesting relations to a number of other areas of physical
mathematics.Comment: 18 pp. Conference Proceeding

### A Comment On Berry Connections

When families of quantum systems are equipped with a continuous family of
Hamiltonians such that there is a gap in the common spectrum one can define a
notion of a Berry connection. In this note we stress that, in general, since
the Hilbert bundle defining the family of quantum systems does not come with a
canonical trivialization there is in fact not a single Berry connection but
rather a family of Berry connections. Two examples illustrate that this remark
can have physical consequences.Comment: 17 pages. V2: Some silly misprints fixe

### Les Houches Lectures on Strings and Arithmetic

These are lecture notes for two lectures delivered at the Les Houches
workshop on Number Theory, Physics, and Geometry, March 2003. They review two
examples of interesting interactions between number theory and string
compactification, and raise some new questions and issues in the context of
those examples. The first example concerns the role of the Rademacher expansion
of coefficients of modular forms in the AdS/CFT correspondence. The second
example concerns the role of the ``attractor mechanism'' of supergravity in
selecting certain arithmetic Calabi-Yau's as distinguished compactifications.Comment: 61pp. harvmac b-mode, 3 figures;v2: minor changes;v3: added refs; v4:
Important mistake concerning the ``Fareytail transform'' has been fixe

### Conformal blocks for AdS5 singletons

We give a simple derivation of the conformal blocks of the singleton sector
of compactifications of IIB string theory on spacetimes of the form X5 x Y5
with Y5 compact, while X5 has as conformal boundary an arbitrary 4-manifold M4.
We retain the second-derivative terms in the action for the B,C fields and thus
the analysis is not purely topological. The unit-normalized conformal blocks
agree exactly with the quantum partition function of the U(1) gauge theory on
the conformal boundary. We reproduce the action of the magnetic translation
group and the SL(2,Z) S-duality group obtained from the purely topological
analysis of Witten. An interesting subtlety in the normalization of the IIB
Chern-Simons phase is noted.Comment: 30pp. late

### Classification of abelian spin Chern-Simons theories

We derive a simple classification of quantum spin Chern-Simons theories with
gauge group T=U(1)^N. While the classical Chern-Simons theories are classified
by an integral lattice the quantum theories are classified differently. Two
quantum theories are equivalent if they have the same invariants on 3-manifolds
with spin structure, or equivalently if they lead to equivalent projective
representations of the modular group. We prove the quantum theory is completely
determined by three invariants which can be constructed from the data in the
classical action. We comment on implications for the classification of
fractional quantum Hall fluids.Comment: 47 pages, 5 figures, LaTe

### Comments On The Two-Dimensional Landau-Ginzburg Approach To Link Homology

We describe rules for computing a homology theory of knots and links in
$\mathbb{R}^3$. It is derived from the theory of framed BPS states bound to
domain walls separating two-dimensional Landau-Ginzburg models with (2,2)
supersymmetry. We illustrate the rules with some sample computations, obtaining
results consistent with Khovanov homology. We show that of the two
Landau-Ginzburg models discussed in this context by Gaiotto and Witten one,
(the so-called Yang-Yang-Landau-Ginzburg model) does not lead to topological
invariants of links while the other, based on a model with target space equal
to the universal cover of the moduli space of $SU(2)$ magnetic monopoles, will
indeed produce a topologically invariant theory of knots and links.Comment: 77 pages, 12 figure

### Crossing the Wall: Branes vs. Bundles

We test a recently proposed wall-crossing formula for the change of the
Hilbert space of BPS states in d=4,N=2 theories. We study decays of D4D2D0
systems into pairs of D4D2D0 systems and we show how the wall-crossing formula
reproduces results of Goettsche and Yoshioka on wall-crossing behavior of the
moduli of slope-stable holomorphic bundles over holomorphic surfaces. Our
comparison shows very clearly that the moduli space of the D4D2D0 system on a
rigid surface in a Calabi-Yau is not the same as the moduli space of torsion
free sheaves, even when worldhseet instantons are neglected. Moreover, we argue
that the physical formula should make some new mathematical predictions for a
future theory of the moduli of stable objects in the derived category.Comment: 23pp. latex, one figur

### A Brief Summary Of Global Anomaly Cancellation In Six-Dimensional Supergravity

This is a short summary of a talk at Strings 2018. See also arXiv:1808.01334.Comment: 16 pages. v2: Minor correction around (5.1). References update

### The Partition Function Of Argyres-Douglas Theory On A Four-Manifold

Using the $u$-plane integral as a tool, we derive a formula for the partition
function of the simplest nontrivial (topologically twisted) Argyres-Douglas
theory on compact, oriented, simply connected, four-manifolds without boundary
and with $b_2^+>0$. The result can be expressed in terms of classical
cohomological invariants and Seiberg-Witten invariants. Our results hint at the
existence of standard four-manifolds that are not of Seiberg-Witten simple
type.Comment: 33 page

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