2,792 research outputs found
T-Branes at the Limits of Geometry
Singular limits of 6D F-theory compactifications are often captured by
T-branes, namely a non-abelian configuration of intersecting 7-branes with a
nilpotent matrix of normal deformations. The long distance approximation of
such 7-branes is a Hitchin-like system in which simple and irregular poles
emerge at marked points of the geometry. When multiple matter fields localize
at the same point in the geometry, the associated Higgs field can exhibit
irregular behavior, namely poles of order greater than one. This provides a
geometric mechanism to engineer wild Higgs bundles. Physical constraints such
as anomaly cancellation and consistent coupling to gravity also limit the order
of such poles. Using this geometric formulation, we unify seemingly different
wild Hitchin systems in a single framework in which orders of poles become
adjustable parameters dictated by tuning gauge singlet moduli of the F-theory
model.Comment: v2: 65 pages, 6 figures, clarifications adde
Conformal Field Theories of Stochastic Loewner Evolutions
Stochastic Loewner evolutions (SLE) are random growth processes of sets,
called hulls, embedded in the two dimensional upper half plane. We elaborate
and develop a relation between SLE evolutions and conformal field theories
(CFT) which is based on a group theoretical formulation of SLE processes and on
the identification of the proper hull boundary states. This allows us to define
an infinite set of SLE zero modes, or martingales, whose existence is a
consequence of the existence of a null vector in the appropriate Virasoro
modules. This identification leads, for instance, to linear systems for
generalized crossing probabilities whose coefficients are multipoint CFT
correlation functions. It provides a direct link between conformal correlation
functions and probabilities of stopping time events in SLE evolutions. We point
out a relation between SLE processes and two dimensional gravity and conjecture
a reconstruction procedure of conformal field theories from SLE data.Comment: 38 pages, 3 figures, to appear in Commun. Math. Phy
Affine holomorphic quantization
We present a rigorous and functorial quantization scheme for affine field
theories, i.e., field theories where local spaces of solutions are affine
spaces. The target framework for the quantization is the general boundary
formulation, allowing to implement manifest locality without the necessity for
metric or causal background structures. The quantization combines the
holomorphic version of geometric quantization for state spaces with the Feynman
path integral quantization for amplitudes. We also develop an adapted notion of
coherent states, discuss vacuum states, and consider observables and their
Berezin-Toeplitz quantization. Moreover, we derive a factorization identity for
the amplitude in the special case of a linear field theory modified by a
source-like term and comment on its use as a generating functional for a
generalized S-matrix.Comment: 42 pages, LaTeX + AMS; v2: expanded to improve readability, new
sections 3.1 (geometric data) and 3.3 (core axioms), minor corrections,
update of references; v3: further update of reference
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