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Quasi BPS Wilson loops, localization of loop equation by homology and exact beta function in the large N limit of SU(N) Yang-Mills theory

Bochicchio, Marco
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.1%
We localize the loop equation of large-N YM theory in the ASD variables on a critical equation for an effective action by means of homological methods as opposed to the cohomological localization of equivariantly closed forms in local field theory. Our localization occurs for some special simple quasi BPS Wilson loops, that have no perimeter divergence and no cusp anomaly for backtracking cusps, in a partial Eguchi-Kawai reduction from four to two dimensions of the non-commutative theory in the limit of infinite non-commutativity and in a lattice regularization in which the ASD integration variables live at the points of the lattice, thus implying an embedding of parabolic Higgs bundles in the YM functional integral. We find that the beta function of the effective action is saturated by the non-commutative ASD vortices of the EK reduction. An exact canonical beta function of NSVZ type that reproduces the universal first and second perturbative coefficients follows by the localization on vortices. Finally we argue that a scheme can be found in which the canonical coupling coincides with the physical charge between static quark sources in the large-N limit and we compare our theoretical calculation with some numerical lattice result.; Comment: 52 pages...

Weak solutions of the cohomological equation on R^2 for regular vector fields

De Leo, Roberto
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 20/01/2014
Relevância na Pesquisa
46.56%
In a recent article, we studied the global solvability of the so-called cohomological equation L_X f=g in C^\infty(\Rt), where X is a regular vector field on the plane and L_X the corresponding Lie derivative. In a joint article with T. Gramchev and A. Kirilov, we studied the existence of global L^1_{loc} weak solutions of the cohomological equation for vector fields depending only on one coordinate. Here we generalize the results of both articles by providing explicit conditions for the existence of global weak solutions to the cohomological equation when X is intrinsically Hamiltonian or of finite type.; Comment: 22 pages, 6 figures

Cohomological equation and cocycle rigidity of parabolic actions in $SL(n,\RR)$

Wang, Zhenqi Jenny
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.6%
For any unitary representation $(\pi,\mathcal{H})$ of $G=SL(n,\RR)$, $n\geq 3$ without non-trivial $G$-invariant vectors, we study smooth solutions of the cohomological equation $\mathfrak{u}f=g$ where $\mathfrak{u}$ is a vector in the root space of $\mathfrak{sl}(n,\RR)$ and $g$ is a given vector in $\mathcal{H}$. We characterize the obstructions to solving the cohomological equation, construct smooth solutions of the cohomological equation and obtain tame Sobolev estimates for $f$. We also study common solutions to (the infinitesimal version of) the cocycle equation $\mathfrak{u}h=\mathfrak{v}g$, where $\mathfrak{u}$ and $\mathfrak{v}$ are commutative vectors in different root spaces of $\mathfrak{sl}(n,\RR)$ and $g$ and $h$ are given vectors in $\mathcal{H}$. We give precisely the condition under which the cocycle equation has common solutions: $(*)$ if $\mathfrak{u}$ and $\mathfrak{v}$ embed in $\mathfrak{sl}(2,\RR)\times \RR$, then the common solution exists. Otherwise, we show counter examples in each $SL(n,\RR)$, $n\geq 3$. As an application, we obtain smooth cocycle rigidity for higher rank parabolic actions over $SL(n,\RR)/\Gamma$, $n\geq 4$ if the Lie algebra of the acting parabolic subgroup contains a pair $\mathfrak{u}$ and $\mathfrak{v}$ satisfying property $(*)$ and prove that the cocycle rigidity fails otherwise. Especially...

On the cohomological equation for interval exchange maps

Marmi, Stefano; Moussa, Pierre; Yoccoz, Jean-Christophe
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 28/04/2003
Relevância na Pesquisa
46.45%
We exhibit an explicit full measure class of minimal interval exchange maps T for which the cohomological equation $\Psi -\Psi\circ T=\Phi$ has a bounded solution $\Psi$ provided that the datum $\Phi$ belongs to a finite codimension subspace of the space of functions having on each interval a derivative of bounded variation. The class of interval exchange maps is characterized in terms of a diophantine condition of ``Roth type'' imposed to an acceleration of the Rauzy--Veech--Zorich continued fraction expansion associated to T. Contents 0. French abridged version 1. Interval exchange maps and the cohomological equation. Main Theorem 2. Rauzy--Veech--Zorich continued fraction algorithm and its acceleration 3. Special Birkhoff sums 4. The Diophantine condition 5. Sketch of the proof of the theorem; Comment: 11 pages, french abstract and abridged version

On the cohomological equation of magnetic flows

Dairbekov, Nurlan S.; Paternain, Gabriel P.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 29/07/2008
Relevância na Pesquisa
46.27%
We consider a magnetic flow without conjugate points on a closed manifold $M$ with generating vector field $\G$. Let $h\in C^{\infty}(M)$ and let $\theta$ be a smooth 1-form on $M$. We show that the cohomological equation \[\G(u)=h\circ \pi+\theta\] has a solution $u\in C^{\infty}(SM)$ only if $h=0$ and $\theta$ is closed. This result was proved in \cite{DP2} under the assumption that the flow of $\G$ is Anosov.

Asymptotics for the wave equation on differential forms on Kerr-de Sitter space

Hintz, Peter; Vasy, Andras
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 10/02/2015
Relevância na Pesquisa
26.16%
We study asymptotics for solutions of Maxwell's equations, in fact of the Hodge-de Rham equation $(d+\delta)u=0$ without restriction on the form degree, on a geometric class of stationary spacetimes with a warped product type structure (without any symmetry assumptions), which in particular include Schwarzschild-de Sitter spaces of all spacetime dimensions $n\geq 4$. We prove that solutions decay exponentially to $0$ or to stationary states in every form degree, and give an interpretation of the stationary states in terms of cohomological information of the spacetime. We also study the wave equation on differential forms and in particular prove analogous results on Schwarzschild-de Sitter spacetimes. We demonstrate the stability of our analysis and deduce asymptotics and decay for solutions of Maxwell's equations, the Hodge-de Rham equation and the wave equation on differential forms on Kerr-de Sitter spacetimes with small angular momentum.; Comment: 43 pages

Cohomological construction of relative twists

Toledano-Laredo, V.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.15%
Let g be a complex, semi-simple Lie algebra, h a Cartan subalgebra of g and D a subdiagram of the Dynkin diagram of g. Let g_D and l_D be the corresponding semi-simple and Levi subalgebras and consider two invariant solutions Phi, Phi_D of the pentagon equation for g and g_D respectively. Motivated by the theory of quasi-Coxeter quasitriangular quasibialgebras \cite{TL3}, we study in this paper the existence of a relative twist, that is an element F invariant under l_D such that the twist of Phi by F is Phi_D. Adapting the method of Donin and Shnider, who treated the case of an empty D, so that l_D=h and Phi_D=1, we give a cohomological construction of such an F under the assumption that Phi_D is the image of Phi under the generalised Harish-Chandra homomorphism. We also show that F is unique up to a gauge transformation if l_D is of corank 1 or F satisfies F^\Theta= F^{21} where \Theta is an involution of g acting as -1 on h.; Comment: minor touch-ups, to appear in Advances in Math

Cohomological equations for suspension flows over Vershik automorphisms

Zubov, Dmitry
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.15%
In this paper we give sufficient conditions for existence of a solution of cohomological equation for suspension flows over automorphisms of Markov compacta, which were introduced by Vershik and Ito. The main result (Theorem 1) can be regarded as a symbolic analogue of results due to Forni and Marmi, Moussa and Yoccoz for translation flows and interval exchange transformations.; Comment: 10 pp. Comments are welcome! ver.2: small corrections are made

The cohomological equation for Roth type interval exchange maps

Marmi, Stefano; Moussa, Pierre; Yoccoz, Jean-Christophe
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 30/03/2004
Relevância na Pesquisa
46.56%
We exhibit an explicit full measure class of minimal interval exchange maps T for which the cohomological equation $\Psi -\Psi\circ T=\Phi$ has a bounded solution $\Psi$ provided that the datum $\Phi$ belongs to a finite codimension subspace of the space of functions having on each interval a derivative of bounded variation. The class of interval exchange maps is characterized in terms of a diophantine condition of ``Roth type'' imposed to an acceleration of the Rauzy--Veech--Zorich continued fraction expansion associated to T. CONTENTS 0. Introduction 1. The continued fraction algorithm for interval exchange maps 1.1 Interval exchnge maps 1.2 The continued fraction algorithm 1.3 Roth type interval exchange maps 2. The cohomological equation 2.1 The theorem of Gottschalk and Hedlund 2.2 Special Birkhoff sums 2.3 Estimates for functions of bounded variation 2.4 Primitives of functions of bounded variation 3. Suspensions of interval exchange maps 3.1 Suspension data 3.2 Construction of a Riemann surface 3.3 Compactification of $M_\zeta^*$ 3.4 The cohomological equation for higher smoothness 4. Proof of full measure for Roth type 4.1 The basic operation of the algorithm for suspensions 4.2 The Teichm\"uller flow 4.3 The absolutely continuous invariant measure 4.4 Integrability of $\log\Vert Z_{(1)}\Vert$ 4.5 Conditions (b) and (c) have full measure 4.6 The main step 4.7 Condition (a) has full measure 4.8 Proof of the Proposition Appendix A Roth--type conditions in a concrete family of i.e.m. Appendix B A non--uniquely ergodic i.e.m. satsfying condition (a) References; Comment: 64 pages...

BCOV theory via Givental group action on cohomological field theories

Shadrin, S.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 03/10/2008
Relevância na Pesquisa
26.15%
In a previous paper (arXiv:0704.1001), Losev, me, and Shneiberg constructed a full descendant potential associated to an arbitrary cyclic Hodge dGBV algebra. This contruction extended the construction of Barannikov and Kontsevich of solution of the WDVV equation, based on the earlier paper of Bershadsky, Cecotti, Ooguri, and Vafa. In the present paper, we give an interpretation of this full descendant potential in terms of Givental group action on cohomological field theories. In particular, the fact that it satisfies all tautological equations becomes a trivial observation.; Comment: 22 pages

Four-dimensional couplings among BF and massless Rarita-Schwinger theories: a BRST cohomological approach

Bizdadea, C.; Cioroianu, E. M.; Saliu, S. O.; Sararu, S. C.; Iordache, M.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 19/12/2008
Relevância na Pesquisa
26.15%
The local and manifestly covariant Lagrangian interactions in four spacetime dimensions that can be added to a free model that describes a massless Rarita-Schwinger theory and an Abelian BF theory are constructed by means of deforming the solution to the master equation on behalf of specific cohomological techniques.; Comment: 59 pages

H\"older regularity of the solutions of the cohomological equation for Roth type interval exchange maps

Marmi, Stefano; Yoccoz, Jean-Christophe
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 07/07/2014
Relevância na Pesquisa
46.27%
We prove that the solutions of the cohomological equation for Roth type interval exchange maps are H\"older continuous provided that the datum is of class $C^r$ with $r>1$ and belongs to a finite-codimension linear subspace.; Comment: 22 pages

The Cohomological Equation and Invariant Distributions for Horocycle Maps

Tanis, James
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.27%
We study the invariant distributions for the horocycle map on $\Gamma\backslash SL(2, \mathbb{R})$ and prove Sobolev estimates for the cohomological equation of the horocycle map. As an application, we obtain an estimate for the rate of equidistribution for horocycle maps on compact manifolds.; Comment: 44 pages

Heterotic horizons, Monge-Ampere equation and del Pezzo surfaces

Gutowski, J.; Papadopoulos, G.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.27%
Heterotic horizons preserving 4 supersymmetries have sections which are T^2 fibrations over 6-dimensional conformally balanced Hermitian manifolds. We give new examples of horizons with sections S^3 X S^3 X T^2 and SU(3). We then examine the heterotic horizons which are T^4 fibrations over a Kahler 4-dimensional manifold. We prove that the solutions depend on 6 functions which are determined by a non-linear differential system of 6 equations that include the Monge-Ampere equation. We show that this system has an explicit solution for the Kahler manifold S^2 X S^2. We also demonstrate that there is an associated cohomological system which has solutions on del Pezzo surfaces. We raise the question of whether for every solution of the cohomological problem there is a solution of the differential system, and so a new heterotic horizon. The horizon sections have topologies which include ((k-1) S^2 X S^4 # k (S^3 X S^3)) X T^2$ indicating the existence of exotic black holes. We also find an example of a horizon section which gives rise to two different near horizon geometries.; Comment: 33 pages, latex. Reference added

Epsilon-neighborhoods of orbits of parabolic diffeomorphisms and cohomological equations

Resman, Maja
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.37%
In this article, we study analyticity properties of (directed) areas of epsilon-neighborhoods of orbits of parabolic germs. The article is motivated by the question of analytic classification using epsilon-neighborhoods of orbits in the simplest formal class. We show that the coefficient in front of epsilon^2 term in the asymptotic expansion in epsilon, which we call the principal part of the area, is a sectorially analytic function of initial point of the orbit. It satisfies a cohomological equation similar to the standard trivialization equation for parabolic diffeomorphisms. We give necessary and sufficient conditions on a diffeomorphism f for the existence of globally analytic solution of this equation. Furthermore, we introduce new classification type for diffeomorphisms implied by this new equation and investigate the relative position of its classes with respect to the analytic classes.; Comment: 41 pages, 1 figures

Quasianalytic monogenic solutions of a cohomological equation

Marmi, Stefano; Sauzin, David
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 18/01/2001
Relevância na Pesquisa
46.51%
We prove that the solutions of a cohomological equation of complex dimension one and in the analytic category have a monogenic dependence on the parameter, and we investigate the question of their quasianalyticity. This equation is the standard linearized conjugacy equation for germs of holomorphic maps in a neighborhood of a fixed point. The parameter is the eigenvalue $q$ of the linear part. This problem has been first investigated by Arnol'd and Herman. Herman raised the question whether the solutions of the cohomological equation had a quasianalytic dependence on the parameter. Indeed they are analytic outside $\S^1$ which is a natural boundary but the solutions are still defined at points of $\S^1$ which lie ``far enough from resonances''. We adapt to our case Herman's construction of an increasing sequence of compacts which avoid resonances and prove that the solutions belong to the associated space of monogenic functions. The solutions admit asymptotic expansions at the points of $\S^1$ which satisfy some arithmetical condition, and Carleman's Theorem allows us to answer negatively to the question of quasianalyticity at these points. But resonances (roots of unity) lead to asymptotic expansions, for which quasianalyticity is obtained as a particular case of \'Ecalle's theory of resurgent functions. At constant-type points one can still recover the solutions from their asymptotic expansions and obtain a special kind of quasianalyticity. Our results are obtained by reducing the problem to the study of a fundamental solution (which is the ``quantum logarithm''). We deduce as a corollary of our work the proof of a conjecture of Gammel on the monogenic and quasianalytic properties of a certain number-theoretical Borel-Wolff-Denjoy series.; Comment: 76 pages...

Sobolev regularity of solutions of the cohomological equation

Forni, Giovanni
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.27%
We refine the theory of the cohomological equation for translation flows on higher genus surfaces with the goal of proving optimal results on the Sobolev regularity of solutions and of distributional obstructions. For typical translation surfaces our results are sharp and we find the expected relation between the regularity of the distributional obstructions and the Lyapunov exponents of the Kontsevich-Zorich renormalization cocycle. As a consequence we exactly determine the dimension of the space of obstructions in each Sobolev regularity class in terms of the Kontsevich-Zorich exponents. For a fixed arbitrary translation surface and a typical direction, our results are probably not optimal but are the best which can be achieved with the available harmonic analysis techniques we have introduced in an earlier paper.; Comment: 119 pages

The cohomological equation for partially hyperbolic diffeomorphisms

Wilkinson, Amie
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 29/09/2008
Relevância na Pesquisa
46.27%
We establish a theory for the existence and regularity of solutions to the cohomological equation over an accessible, partially hyperbolic diffeomorphism. As a by-product of our techniques, we show that for $r>1$, any $C^r$ homogeneous, locally compact submanifold of a $C^r$ manifold is in fact a $C^r$ submanifold.; Comment: 94 pages, 8 figures

Interacting mixed-symmetry type tensor gauge fields of degrees two and three: a four-dimensional cohomological approach

Bizdadea, C.; Ciobirca, C. C.; Cioroianu, E. M.; Saliu, S. O.; Sararu, S. C.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 10/03/2003
Relevância na Pesquisa
26.15%
A special class of mixed-symmetry type tensor gauge fields of degrees two and three in four dimensions is investigated from the perspective of the Lagrangian deformation procedure based on cohomological BRST techniques. It is shown that the deformed solution to the master equation can be taken to be nonvanishing only at the first order in the coupling constant. As a consequence, we deduce an interacting model with deformed gauge transformations, an open gauge algebra and undeformed reducibility functions. The resulting coupled Lagrangian action contains a quartic vertex and some ``mass'' terms involving only the tensor of degree two. We discuss in what sense the results of the deformation procedure derived here are complementary to recent others.; Comment: LaTeX 2.e, 10 pages

Equidistribution for higher-rank Abelian actions on Heisenberg nilmanifolds

Flaminio, Livio; Cosentino, Salvatore
Fonte: American Institute of Mathematical Sciences Publicador: American Institute of Mathematical Sciences
Tipo: Artigo de Revista Científica
Publicado em /11/2015 ENG
Relevância na Pesquisa
36.15%
2010 Mathematics Subject Classification: Primary: 37C85, 37A17, 37A45; Secondary: 11K36, 11L07.; We prove quantitative equidistribution results for actions of Abelian subgroups of the (2g + 1)-dimensional Heisenberg group acting on compact (2g + 1)-dimensional homogeneous nilmanifolds. The results are based on the study of the C∞-cohomology of the action of such groups, on tame estimates of the associated cohomological equations and on a renormalization method initially applied by Forni to surface flows and by Forni and the second author to other parabolic flows. As an application we obtain bounds for finite Theta sums defined by real quadratic forms in g variables, generalizing the classical results of Hardy and Littlewood [25, 26] and the optimal result of Fiedler, Jurkat, and Körner [17] to higher dimension.