4,517 research outputs found
The Omega Deformation, Branes, Integrability, and Liouville Theory
We reformulate the Omega-deformation of four-dimensional gauge theory in a
way that is valid away from fixed points of the associated group action. We use
this reformulation together with the theory of coisotropic A-branes to explain
recent results linking the Omega-deformation to integrable Hamiltonian systems
in one direction and Liouville theory of two-dimensional conformal field theory
in another direction.Comment: 96 p
Exact Resummations in the Theory of Hydrodynamic Turbulence: III. Scenarios for Anomalous Scaling and Intermittency
Elements of the analytic structure of anomalous scaling and intermittency in
fully developed hydrodynamic turbulence are described. We focus here on the
structure functions of velocity differences that satisfy inertial range scaling
laws , and the correlation of energy dissipation
. The goal is to understand the
exponents and from first principles. In paper II of this series
it was shown that the existence of an ultraviolet scale (the dissipation scale
) is associated with a spectrum of anomalous exponents that characterize
the ultraviolet divergences of correlations of gradient fields. The leading
scaling exponent in this family was denoted . The exact resummation of
ladder diagrams resulted in the calculation of which satisfies the
scaling relation . In this paper we continue our analysis and
show that nonperturbative effects may introduce multiscaling (i.e.
not being linear in ) with the renormalization scale being the infrared
outer scale of turbulence . It is shown that deviations from K41 scaling of
() must appear if the correlation of dissipation is
mixing (i.e. ). We derive an exact scaling relation . We present analytic expressions for for all
and discuss their relation to experimental data. One surprising prediction is
that the time decay constant of scales
independently of : the dynamic scaling exponent is the same for all
-order quantities, .Comment: PRE submitted, 22 pages + 11 figures, REVTeX. The Eps files of
figures will be FTPed by request to [email protected]
From SO/Sp instantons to W-algebra blocks
We study instanton partition functions for N=2 superconformal Sp(1) and SO(4)
gauge theories. We find that they agree with the corresponding U(2) instanton
partitions functions only after a non-trivial mapping of the microscopic gauge
couplings, since the instanton counting involves different renormalization
schemes. Geometrically, this mapping relates the Gaiotto curves of the
different realizations as double coverings. We then formulate an AGT-type
correspondence between Sp(1)/SO(4) instanton partition functions and chiral
blocks with an underlying W(2,2)-algebra symmetry. This form of the
correspondence eliminates the need to divide out extra U(1) factors. Finally,
to check this correspondence for linear quivers, we compute expressions for the
Sp(1)-SO(4) half-bifundamental.Comment: 83 pages, 29 figures; minor change
Invariance of immersed Floer cohomology under Lagrangian surgery
We show that cellular Floer cohomology of an immersed Lagrangian brane is
invariant under smoothing of a self-intersection point if the quantum valuation
of the weakly bounding cochain vanishes and the Lagrangian has dimension at
least two. The chain-level map replaces the two orderings of the
self-intersection point with meridianal and longitudinal cells on the handle
created by the surgery, and uses a bijection between holomorphic disks
developed by Fukaya-Oh-Ohta-Ono. Our result generalizes invariance of
potentials for certain Lagrangian surfaces in
Dimitroglou-Rizell--Ekholm--Tonkonog, and implies the invariance of Floer
cohomology under mean curvature flow with this type of surgery, as conjectured
by Joyce.Comment: 100 pages. This version has minor corrections (one which was in the
isomorphism of Floer cohomologies, but which did not affect the main result.
Degenerate Operators and the Expansion: Lorentzian Resummations, High Order Computations, and Super-Virasoro Blocks
One can obtain exact information about Virasoro conformal blocks by
analytically continuing the correlators of degenerate operators. We argued in
recent work that this technique can be used to explicitly resolve information
loss problems in AdS/CFT. In this paper we use the technique to perform
calculations in the small expansion: (1) we prove the
all-orders resummation of logarithmic factors in
the Lorentzian regime, demonstrating that corrections directly shift
Lyapunov exponents associated with chaos, as claimed in prior work, (2) we
perform another all-orders resummation in the limit of large with fixed
, interpolating between the early onset of chaos and late time behavior,
(3) we explicitly compute the Virasoro vacuum block to order and
, corresponding to and loop calculations in AdS, and (4) we
derive the heavy-light vacuum blocks in theories with
superconformal symmetry.Comment: 34+20 pages, 2 figure
Big Bang, Blowup, and Modular Curves: Algebraic Geometry in Cosmology
We introduce some algebraic geometric models in cosmology related to the
"boundaries" of space-time: Big Bang, Mixmaster Universe, Penrose's crossovers
between aeons. We suggest to model the kinematics of Big Bang using the
algebraic geometric (or analytic) blow up of a point . This creates a
boundary which consists of the projective space of tangent directions to
and possibly of the light cone of . We argue that time on the boundary
undergoes the Wick rotation and becomes purely imaginary. The Mixmaster
(Bianchi IX) model of the early history of the universe is neatly explained in
this picture by postulating that the reverse Wick rotation follows a hyperbolic
geodesic connecting imaginary time axis to the real one. Penrose's idea to see
the Big Bang as a sign of crossover from "the end of previous aeon" of the
expanding and cooling Universe to the "beginning of the next aeon" is
interpreted as an identification of a natural boundary of Minkowski space at
infinity with the Big Bang boundary
Motives: an introductory survey for physicists
We survey certain accessible aspects of Grothendieck's theory of motives in
arithmetic algebraic geometry for mathematical physicists, focussing on areas
that have recently found applications in quantum field theory. An appendix (by
Matilde Marcolli) sketches further connections between motivic theory and
theoretical physics.Comment: LaTeX 35 pages, article by Abhijnan Rej with an appendix by
M.Marcolli. Version II/Final: cosmetic changes to bibliography, added a small
subsection on triangulated categories to section 6. Accepted for publication
in the MPIM-Bonn "Renormalization, combinatorics and physics" proceedings
volum
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