25,754 research outputs found

### Wilson-'t Hooft operators in four-dimensional gauge theories and S-duality

We study operators in four-dimensional gauge theories which are localized on
a straight line, create electric and magnetic flux, and in the UV limit break
the conformal invariance in the minimal possible way. We call them Wilson-'t
Hooft operators, since in the purely electric case they reduce to the
well-known Wilson loops, while in general they may carry 't Hooft magnetic
flux. We show that to any such operator one can associate a maximally symmetric
boundary condition for gauge fields on AdS^2\times S^2. We show that Wilson-'t
Hooft operators are classifed by a pair of weights (electric and magnetic) for
the gauge group and its magnetic dual, modulo the action of the Weyl group. If
the magnetic weight does not belong to the coroot lattice of the gauge group,
the corresponding operator is topologically nontrivial (carries nonvanishing 't
Hooft magnetic flux). We explain how the spectrum of Wilson-'t Hooft operators
transforms under the shift of the theta-angle by 2\pi. We show that, depending
on the gauge group, either SL(2,Z) or one of its congruence subgroups acts in a
natural way on the set of Wilson-'t Hooft operators. This can be regarded as
evidence for the S-duality of N=4 super-Yang-Mills theory. We also compute the
one-point function of the stress-energy tensor in the presence of a Wilson-'t
Hooft operator at weak coupling.Comment: 32 pages, latex. v2: references added. v3: numerical factors
corrected, other minor change

### Unified Einstein-Virasoro Master Equation in the General Non-Linear Sigma Model

The Virasoro master equation (VME) describes the general affine-Virasoro
construction T=L^{ab}J_aJ_b+iD^a \dif J_a in the operator algebra of the WZW
model, where $L^{ab}$ is the inverse inertia tensor and $D^a$ is the
improvement vector. In this paper, we generalize this construction to find the
general (one-loop) Virasoro construction in the operator algebra of the general
non-linear sigma model. The result is a unified Einstein-Virasoro master
equation which couples the spacetime spin-two field $L^{ab}$ to the background
fields of the sigma model. For a particular solution $L_G^{ab}$, the unified
system reduces to the canonical stress tensors and conventional Einstein
equations of the sigma model, and the system reduces to the general
affine-Virasoro construction and the VME when the sigma model is taken to be
the WZW action. More generally, the unified system describes a space of
conformal field theories which is presumably much larger than the sum of the
general affine-Virasoro construction and the sigma model with its canonical
stress tensors. We also discuss a number of algebraic and geometrical
properties of the system, including its relation to an unsolved problem in the
theory of $G$-structures on manifolds with torsion.Comment: LaTeX, 55 pages, one postscript figure, uses epsfig.sty. contains a
few minor corrections; version to be published in Int. J. Mod. Phys.

### Cancellation of quantum mechanical higher loop contributions to the gravitational chiral anomaly

We give an explicit demonstration, using the rigorous Feynman rules developed
in~\0^{1}, that the regularized trace \tr \gamma_5 e^{-\beta \Dslash^2} for
the gravitational chiral anomaly expressed as an appropriate quantum mechanical
path integral is $\beta$-independent up to two-loop level. Identities and
diagrammatic notations are developed to facilitate rapid evaluation of graphs
given by these rules.Comment: 10 pages, LaTeX and psfig (many figures

### The orbifold-string theories of permutation-type: II. Cycle dynamics and target space-time dimensions

We continue our discussion of the general bosonic prototype of the new
orbifold-string theories of permutation type. Supplementing the extended
physical-state conditions of the previous paper, we construct here the extended
Virasoro generators with cycle central charge
$\hat{c}_j(\sigma)=26f_j(\sigma)$, where $f_j(\sigma)$ is the length of cycle
$j$ in twisted sector $\sigma$. We also find an equivalent, reduced formulation
of each physical-state problem at reduced cycle central charge
$c_j(\sigma)=26$. These tools are used to begin the study of the target
space-time dimension $\hat{D}_j(\sigma)$ of cycle $j$ in sector $\sigma$, which
is naturally defined as the number of zero modes (momenta) of each cycle. The
general model-dependent formulae derived here will be used extensively in
succeeding papers, but are evaluated in this paper only for the simplest case
of the "pure" permutation orbifolds.Comment: 32 page

### New Duality Transformations in Orbifold Theory

We find new duality transformations which allow us to construct the stress
tensors of all the twisted sectors of any orbifold A(H)/H, where A(H) is the
set of all current-algebraic conformal field theories with a finite symmetry
group H \subset Aut(g). The permutation orbifolds with H = Z_\lambda and H =
S_3 are worked out in full as illustrations but the general formalism includes
both simple and semisimple g. The motivation for this development is the
recently-discovered orbifold Virasoro master equation, whose solutions are
identified by the duality transformations as sectors of the permutation
orbifolds A(D_\lambda)/Z_\lambda.Comment: 48 pages,typos correcte

### Black Hole Meiosis

The enumeration of BPS bound states in string theory needs refinement.
Studying partition functions of particles made from D-branes wrapped on
algebraic Calabi-Yau 3-folds, and classifying states using split attractor flow
trees, we extend the method for computing a refined BPS index, arXiv:0810.4301.
For certain D-particles, a finite number of microstates, namely polar states,
exclusively realized as bound states, determine an entire partition function
(elliptic genus). This underlines their crucial importance: one might call them
the `chromosomes' of a D-particle or a black hole. As polar states also can be
affected by our refinement, previous predictions on elliptic genera are
modified. This can be metaphorically interpreted as `crossing-over in the
meiosis of a D-particle'. Our results improve on hep-th/0702012, provide
non-trivial evidence for a strong split attractor flow tree conjecture, and
thus suggest that we indeed exhaust the BPS spectrum. In the D-brane
description of a bound state, the necessity for refinement results from the
fact that tachyonic strings split up constituent states into `generic' and
`special' states. These are enumerated separately by topological invariants,
which turn out to be partitions of Donaldson-Thomas invariants. As modular
predictions provide a check on many of our results, we have compelling evidence
that our computations are correct.Comment: 46 pages, 8 figures. v2: minor changes. v3: minor changes and
reference adde

### Enantiomer fractions instead of enantiomer ratios

The use of enantiomer ratios (ERs) to indicate the relative amounts of a pair of enantiomers in a sample has some disadvantages. Enantiomer fractions (EFs) are proposed as all alternative expression to eliminate the difficulties. (C) 2000 Elsevier Science Ltd

### Twisted Open Strings from Closed Strings: The WZW Orientation Orbifolds

Including {\it world-sheet orientation-reversing automorphisms}
$\hat{h}_{\sigma} \in H_-$ in the orbifold program, we construct the operator
algebras and twisted KZ systems of the general WZW {\it orientation orbifold}
$A_g (H_-) /H_-$. We find that the orientation-orbifold sectors corresponding
to each $\hat{h}_{\sigma} \in H_-$ are {\it twisted open} WZW strings, whose
properties are quite distinct from conventional open-string orientifold
sectors. As simple illustrations, we also discuss the classical (high-level)
limit of our construction and free-boson examples on abelian $g$.Comment: 65 pages, typos correcte

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