12,290 research outputs found
Twisted Open Strings from Closed Strings: The WZW Orientation Orbifolds
Including {\it world-sheet orientation-reversing automorphisms}
in the orbifold program, we construct the operator
algebras and twisted KZ systems of the general WZW {\it orientation orbifold}
. We find that the orientation-orbifold sectors corresponding
to each 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 .Comment: 65 pages, typos correcte
Generalized Fibonacci numbers and extreme value laws for the Rényi map
In this paper we prove an extreme value law for a stochastic process obtained by iterating the Rényi map x↦βx(mod1), where we assume that β>1 is an integer. Haiman (2018) derived a recursion formula for the Lebesgue measure of threshold exceedance sets. We show how this recursion formula is related to a rescaled version of the k-generalized Fibonacci sequence. For the latter sequence we derive a Binet formula which leads to a closed-form expression for the distribution of partial maxima of the stochastic process. The proof of the extreme value law is completed by deriving sharp bounds for the dominant root of the characteristic polynomial associated with the Fibonacci sequence
Two Large Examples in Orbifold Theory: Abelian Orbifolds and the Charge Conjugation Orbifold on su(n)
Recently the operator algebra and twisted vertex operator equations were
given for each sector of all WZW orbifolds, and a set of twisted KZ equations
for the WZW permutation orbifolds were worked out as a large example. In this
companion paper we report two further large examples of this development. In
the first example we solve the twisted vertex operator equations in an abelian
limit to obtain the twisted vertex operators and correlators of a large class
of abelian orbifolds. In the second example, the twisted vertex operator
equations are applied to obtain a set of twisted KZ equations for the
(outer-automorphic) charge conjugation orbifold on su(n \geq 3).Comment: 58 pages, v2: three minor typo
Membranes for Topological M-Theory
We formulate a theory of topological membranes on manifolds with G_2
holonomy. The BRST charges of the theories are the superspace Killing vectors
(the generators of global supersymmetry) on the background with reduced
holonomy G_2. In the absence of spinning formulations of supermembranes, the
starting point is an N=2 target space supersymmetric membrane in seven
euclidean dimensions. The reduction of the holonomy group implies a twisting of
the rotations in the tangent bundle of the branes with ``R-symmetry'' rotations
in the normal bundle, in contrast to the ordinary spinning formulation of
topological strings, where twisting is performed with internal U(1) currents of
the N=(2,2) superconformal algebra. The double dimensional reduction on a
circle of the topological membrane gives the strings of the topological A-model
(a by-product of this reduction is a Green-Schwarz formulation of topological
strings). We conclude that the action is BRST-exact modulo topological terms
and fermionic equations of motion. We discuss the role of topological membranes
in topological M-theory and the relation of our work to recent work by Hitchin
and by Dijkgraaf et al.Comment: 22 pp, plain tex. v2: refs. adde
The Operator Algebra and Twisted KZ Equations of WZW Orbifolds
We obtain the operator algebra of each twisted sector of all WZW orbifolds,
including the general twisted current algebra and the algebra of the twisted
currents with the twisted affine primary fields. Surprisingly, the twisted
right and left mover current algebras are not a priori copies of each other.
Using the operator algebra we also derive world-sheet differential equations
for the twisted affine primary fields of all WZW orbifolds. Finally we include
ground state properties to obtain the twisted Knizhnik-Zamolodchikov equations
of the WZW permutation orbifolds and the inner-automorphic WZW orbifolds.Comment: Latex, 88 pages. added a comment on outer automorphic orbifolds and
one reference; v3: minor typos correcte
Noncommutativity relations in type IIB theory and their supersymmetry
In the present paper we investigate noncommutativity of and -brane
world-volumes embedded in space-time of type IIB superstring theory. Boundary
conditions, which preserve half of the initial supersymmetry, are treated as
canonical constraints. Solving the constraints we obtain original coordinates
in terms of the effective coordinates and momenta. Presence of momenta induces
noncommutativity of string endpoints. We show that noncommutativity relations
are connected by N=1 supersymmetry transformations and noncommutativity
parameters are components of N=1 supermultiplet
Supersymmetry and LHC
The motivation for introduction of supersymmetry in high energy physics as
well as a possibility for supersymmetry discovery at LHC (Large Hadronic
Collider) are discussed. The main notions of the Minimal Supersymmetric
Standard Model (MSSM) are introduced. Different regions of parameter space are
analyzed and their phenomenological properties are compared. Discovery
potential of LHC for the planned luminosity is shown for different channels.
The properties of SUSY Higgs bosons are studied and perspectives of their
observation at LHC are briefly outlined.Comment: Lectures given at the 9th Moscow International School of Physics
(XXXIV ITEP Winter School of Physics
Holographic Thermalization
Using the AdS/CFT correspondence, we probe the scale-dependence of
thermalization in strongly coupled field theories following a quench, via
calculations of two-point functions, Wilson loops and entanglement entropy in
d=2,3,4. In the saddlepoint approximation these probes are computed in AdS
space in terms of invariant geometric objects - geodesics, minimal surfaces and
minimal volumes. Our calculations for two-dimensional field theories are
analytical. In our strongly coupled setting, all probes in all dimensions share
certain universal features in their thermalization: (1) a slight delay in the
onset of thermalization, (2) an apparent non-analyticity at the endpoint of
thermalization, (3) top-down thermalization where the UV thermalizes first. For
homogeneous initial conditions the entanglement entropy thermalizes slowest,
and sets a timescale for equilibration that saturates a causality bound over
the range of scales studied. The growth rate of entanglement entropy density is
nearly volume-independent for small volumes, but slows for larger volumes.Comment: 39 pages, 24 figure
Transverse momentum dependent parton distributions in a light-cone quark model
The leading twist transverse momentum dependent parton distributions (TMDs)
are studied in a light-cone description of the nucleon where the Fock expansion
is truncated to consider only valence quarks. General analytic expressions are
derived in terms of the six amplitudes needed to describe the three-quark
sector of the nucleon light-cone wave function. Numerical calculations for the
T-even TMDs are presented in a light-cone constituent quark model, and the role
of the so-called pretzelosity is investigated to produce a nonspherical shape
of the nucleon.Comment: references added and typos corrected; version to appear in Phys. Rev.
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