11,220 research outputs found
Chiral Observables and Modular Invariants
Various definitions of chiral observables in a given Moebius covariant
two-dimensional theory are shown to be equivalent. Their representation theory
in the vacuum Hilbert space of the 2D theory is studied. It shares the general
characteristics of modular invariant partition functions, although SL(2,Z)
transformation properties are not assumed. First steps towards classification
are made.Comment: 28 pages, 1 figur
Some Nearly Quantum Theories
We consider possible non-signaling composites of probabilistic models based
on euclidean Jordan algebras. Subject to some reasonable constraints, we show
that no such composite exists having the exceptional Jordan algebra as a direct
summand. We then construct several dagger compact categories of such
Jordan-algebraic models. One of these neatly unifies real, complex and
quaternionic mixed-state quantum mechanics, with the exception of the
quaternionic "bit". Another is similar, except in that (i) it excludes the
quaternionic bit, and (ii) the composite of two complex quantum systems comes
with an extra classical bit. In both of these categories, states are morphisms
from systems to the tensor unit, which helps give the categorical structure a
clear operational interpretation. A no-go result shows that the first of these
categories, at least, cannot be extended to include spin factors other than the
(real, complex, and quaternionic) quantum bits, while preserving the
representation of states as morphisms. The same is true for attempts to extend
the second category to even-dimensional spin-factors. Interesting phenomena
exhibited by some composites in these categories include failure of local
tomography, supermultiplicativity of the maximal number of mutually
distinguishable states, and mixed states whose marginals are pure.Comment: In Proceedings QPL 2015, arXiv:1511.0118
Exploring the Vacuum Geometry of N=1 Gauge Theories
Using techniques of algorithmic algebraic geometry, we present a new and
efficient method for explicitly computing the vacuum space of N=1 gauge
theories. We emphasize the importance of finding special geometric properties
of these spaces in connecting phenomenology to guiding principles descending
from high-energy physics. We exemplify the method by addressing various
subsectors of the MSSM. In particular the geometry of the vacuum space of
electroweak theory is described in detail, with and without right-handed
neutrinos. We discuss the impact of our method on the search for evidence of
underlying physics at a higher energy. Finally we describe how our results can
be used to rule out certain top-down constructions of electroweak physics.Comment: 35 pages, 2 figures, LaTe
Mass Degeneracies In Self-Dual Models
An algebraic restriction of the nonabelian self-dual Chern-Simons-Higgs
systems leads to coupled abelian models with interesting mass spectra. The
vacua are characterized by embeddings of into the gauge algebra, and in
the broken phases the gauge and real scalar masses coincide, reflecting the
relation of these self-dual models to SUSY. The masses themselves are
related to the exponents of the gauge algebra, and the self-duality equation is
a deformation of the classical Toda equations.Comment: 10 pages LaTeX (previous copy truncated
Schwinger-Keldysh formalism II: Thermal equivariant cohomology
Causally ordered correlation functions of local operators in near-thermal
quantum systems computed using the Schwinger-Keldysh formalism obey a set of
Ward identities. These can be understood rather simply as the consequence of a
topological (BRST) algebra, called the universal Schwinger-Keldysh
superalgebra, as explained in our companion paper arXiv:1610.01940. In the
present paper we provide a mathematical discussion of this topological algebra.
In particular, we argue that the structures can be understood in the language
of extended equivariant cohomology. To keep the discussion self-contained, we
provide a basic review of the algebraic construction of equivariant cohomology
and explain how it can be understood in familiar terms as a superspace gauge
algebra. We demonstrate how the Schwinger-Keldysh construction can be
succinctly encoded in terms a thermal equivariant cohomology algebra which
naturally acts on the operator (super)-algebra of the quantum system. The main
rationale behind this exploration is to extract symmetry statements which are
robust under renormalization group flow and can hence be used to understand
low-energy effective field theory of near-thermal physics. To illustrate the
general principles, we focus on Langevin dynamics of a Brownian particle,
rephrasing some known results in terms of thermal equivariant cohomology. As
described elsewhere, the general framework enables construction of effective
actions for dissipative hydrodynamics and could potentially illumine our
understanding of black holes.Comment: 72 pages; v2: fixed typos. v3: minor clarifications and improvements
to non-equilbirum work relations discussion. v4: typos fixed. published
versio
Classical backgrounds and scattering for affine Toda theory on a half-line
We find classical solutions to the simply-laced affine Toda equations which
satisfy integrable boundary conditions using solitons which are analytically
continued from imaginary coupling theories. Both static `vacuum' configurations
and the time-dependent perturbations about them which correspond to classical
vacua and particle scattering solutions respectively are considered. A large
class of classical scattering matrices are calculated and found to satisfy the
reflection bootstrap equation.Comment: Latex document, 28 pages, 3 figures include
A magic pyramid of supergravities
By formulating N = 1, 2, 4, 8, D = 3, Yang-Mills with a single Lagrangian and
single set of transformation rules, but with fields valued respectively in
R,C,H,O, it was recently shown that tensoring left and right multiplets yields
a Freudenthal-Rosenfeld-Tits magic square of D = 3 supergravities. This was
subsequently tied in with the more familiar R,C,H,O description of spacetime to
give a unified division-algebraic description of extended super Yang-Mills in D
= 3, 4, 6, 10. Here, these constructions are brought together resulting in a
magic pyramid of supergravities. The base of the pyramid in D = 3 is the known
4x4 magic square, while the higher levels are comprised of a 3x3 square in D =
4, a 2x2 square in D = 6 and Type II supergravity at the apex in D = 10. The
corresponding U-duality groups are given by a new algebraic structure, the
magic pyramid formula, which may be regarded as being defined over three
division algebras, one for spacetime and each of the left/right Yang-Mills
multiplets. We also construct a conformal magic pyramid by tensoring conformal
supermultiplets in D = 3, 4, 6. The missing entry in D = 10 is suggestive of an
exotic theory with G/H duality structure F4(4)/Sp(3) x Sp(1).Comment: 30 pages, 6 figures. Updated to match published version. References
and comments adde
Summing the Instantons: Quantum Cohomology and Mirror Symmetry in Toric Varieties
We use the gauged linear sigma model introduced by Witten to calculate
instanton expansions for correlation functions in topological sigma models with
target space a toric variety or a Calabi--Yau hypersurface .
In the linear model the instanton moduli spaces are relatively simple objects
and the correlators are explicitly computable; moreover, the instantons can be
summed, leading to explicit solutions for both kinds of models. In the case of
smooth , our results reproduce and clarify an algebraic solution of the
model due to Batyrev. In addition, we find an algebraic relation determining
the solution for in terms of that for . Finally, we propose a
modification of the linear model which computes instanton expansions about any
limiting point in the moduli space. In the smooth case this leads to a (second)
algebraic solution of the model. We use this description to prove some
conjectures about mirror symmetry, including the previously conjectured
``monomial-divisor mirror map'' of Aspinwall, Greene, and Morrison.Comment: 91 pages and 3 figures, harvmac with epsf (Changes in this version:
one minor correction, one clarification, one new reference
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