150 research outputs found
Givental graphs and inversion symmetry
Inversion symmetry is a very non-trivial discrete symmetry of Frobenius
manifolds. It was obtained by Dubrovin from one of the elementary Schlesinger
transformations of a special ODE associated to a Frobenius manifold. In this
paper, we review the Givental group action on Frobenius manifolds in terms of
Feynman graphs and obtain an interpretation of the inversion symmetry in terms
of the action of the Givental group. We also consider the implication of this
interpretation of the inversion symmetry for the Schlesinger transformations
and for the Hamiltonians of the associated principle hierarchy.Comment: 26 pages; revised according to the referees' remark
Enhanced Worldvolume Supersymmetry and Intersecting Domain Walls in N=1 SQCD
We study the worldvolume dynamics of BPS domain walls in N=1 SQCD with N_f=N
flavors, and exhibit an enhancement of supersymmetry for the reduced moduli
space associated with broken flavor symmetries. We provide an explicit
construction of the worldvolume superalgebra which corresponds to an N=2 Kahler
sigma model in 2+1D deformed by a potential, given by the norm squared of a
U(1) Killing vector, resulting from the flavor symmetries broken by unequal
quark masses. This framework leads to a worldvolume description of novel
two-wall junction configurations, which are 1/4-BPS objects, but nonetheless
preserve two supercharges when viewed as kinks on the wall worldvolume.Comment: 35 pages, 3 figures; v2: minor corrections and a reference added, to
appear in Phys. Rev.
Hypercommutative operad as a homotopy quotient of BV
We give an explicit formula for a quasi-isomorphism between the operads
Hycomm (the homology of the moduli space of stable genus 0 curves) and
BV/ (the homotopy quotient of Batalin-Vilkovisky operad by the
BV-operator). In other words we derive an equivalence of Hycomm-algebras and
BV-algebras enhanced with a homotopy that trivializes the BV-operator.
These formulas are given in terms of the Givental graphs, and are proved in
two different ways. One proof uses the Givental group action, and the other
proof goes through a chain of explicit formulas on resolutions of Hycomm and
BV. The second approach gives, in particular, a homological explanation of the
Givental group action on Hycomm-algebras.Comment: minor corrections added, to appear in Comm.Math.Phy
On two-dimensional quantum gravity and quasiclassical integrable hierarchies
The main results for the two-dimensional quantum gravity, conjectured from
the matrix model or integrable approach, are presented in the form to be
compared with the world-sheet or Liouville approach. In spherical limit the
integrable side for minimal string theories is completely formulated using
simple manipulations with two polynomials, based on residue formulas from
quasiclassical hierarchies. Explicit computations for particular models are
performed and certain delicate issues of nontrivial relations among them are
discussed. They concern the connections between different theories, obtained as
expansions of basically the same stringy solution to dispersionless KP
hierarchy in different backgrounds, characterized by nonvanishing background
values of different times, being the simplest known example of change of the
quantum numbers of physical observables, when moving to a different point in
the moduli space of the theory.Comment: 20 pages, based on talk presented at the conference "Liouville field
theory and statistical models", dedicated to the memory of Alexei
Zamolodchikov, Moscow, June 200
Making the Best of Polymers with Sulfur–Nitrogen Bonds: From Sources to Innovative Materials
Polymers with sulfur–nitrogen bonds have been underestimated for a long time, although the intrinsic characteristics of these polymers offer a myriad of superior properties (e.g., degradation, flame retardancy, film‐forming ability, good solubility in polar solvents, and high refractivity with small chromatic dispersions, among other things) compared to their carbon analogues. The remarkable characteristics of these polymers result from the unique chemical properties of the sulfur–nitrogen bond (e.g., its polar character and the multiple valence states of sulfur), and thus open excellent perspectives for the development of innovative (bio)materials. Accordingly, this review describes the most common chemical approaches toward the efficient synthesis of these ubiquitous polymers possessing diverse sulfur–nitrogen bonds, and furthermore highlights their applications in multiple fields, ranging from biomedicine to energy storage, with the aim of providing an informative perspective on challenges facing the synthesis of sulfur–nitrogen polymers with desirable properties
Refined Cigar and Omega-deformed Conifold
Antoniadis et al proposed a relation between the Omega-deformation and
refined correlation functions of the topological string theory. We investigate
the proposal for the deformed conifold geometry from a non-compact Gepner model
approach. The topological string theory on the deformed conifold has a dual
description in terms of the c=1 non-critical string theory at the self-dual
radius, and the Omega-deformation yields the radius deformation. We show that
the refined correlation functions computed from the twisted SL(2,R)/U(1)
Kazama-Suzuki coset model at level k=1 have direct c=1 non-critical string
theory interpretations. After subtracting the leading singularity to procure
the 1PI effective action, we obtain the agreement with the proposal.Comment: 15 pages, v2: reference added, v3: published versio
Topological Landau-Ginzburg theory with a rational potential and the dispersionless KP hierarchy
Based on the dispersionless KP (dKP) theory, we give a comprehensive study of
the topological Landau-Ginzburg (LG) theory characterized by a rational
potential. Writing the dKP hierarchy in a general form, we find that the
hierarchy naturally includes the dispersionless (continuous) limit of Toda
hierarchy and its generalizations having finite number of primaries. Several
flat solutions of the topological LG theory are obtained in this formulation,
and are identified with those discussed by Dubrovin. We explicitly construct
gravitational descendants for all the primary fields. Giving a residue formula
for the 3-point functions of the fields, we show that these 3-point functions
satisfy the topological recursion relation. The string equation is obtained as
the generalized hodograph solutions of the dKP hierarchy, which show that all
the gravitational effects to the constitutive equations (2-point functions) can
be renormalized into the coupling constants in the small phase space.Comment: 54 pages, Plain TeX. Figure could be obtained from Kodam
Vortex Strings and Four-Dimensional Gauge Dynamics
We study the low-energy quantum dynamics of vortex strings in the Higgs phase
of N=2 supersymmetric QCD. The exact BPS spectrum of the stretched string is
shown to coincide with the BPS spectrum of the four-dimensional parent gauge
theory. Perturbative string excitations correspond to bound W-bosons and quarks
while the monopoles appear as kinks on the vortex string. This provides a
physical explanation for an observation by N. Dorey relating the quantum
spectra of theories in two and four dimensions.Comment: 23 pages, 1 figure. v2: Two extra appendices included: one on the
brane construction, the other describing the potential on the vortex moduli
space. Two figures added. Typos corrected and references added. v3: BPS
nature of quarks correcte
Quantum deformations of associative algebras and integrable systems
Quantum deformations of the structure constants for a class of associative
noncommutative algebras are studied. It is shown that these deformations are
governed by the quantum central systems which has a geometrical meaning of
vanishing Riemann curvature tensor for Christoffel symbols identified with the
structure constants. A subclass of isoassociative quantum deformations is
described by the oriented associativity equation and, in particular, by the
WDVV equation. It is demonstrated that a wider class of weakly (non)associative
quantum deformations is connected with the integrable soliton equations too. In
particular, such deformations for the three-dimensional and
infinite-dimensional algebras are described by the Boussinesq equation and KP
hierarchy, respectively.Comment: Numeration of the formulas is correcte
Target space symmetries in topological theories I
We study realization of the target space diffeomorphisms in the type
topological string. We found that the charges, which generate transformations
of the boundary observables, form an algebra, which differs from that of bulk
charges by the contribution of the bubbled disks. We discuss applications to
noncommutative field theories.Comment: 22pp, one picture; refs added, typos correcte
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