55788912
On Twisted N = 2 5D Super Yang–Mills Theory
On a five-dimensional simply connected Sasaki–Einstein manifold, one can construct Yang–Mills theories coupled to matter with at least two supersymmetries. The partition function of these theories localises on the contact instantons, however, the contact instanton equations are not elliptic. It turns out that these equations can be embedded into the Haydys–Witten equations (which are elliptic) in the same way the 4D anti-self-dual instanton equations are embedded in the Vafa–Witten equations. We show that under some favourable circumstances, the latter equations will reduce to the former by proving some vanishing theorems. It was also known that the Haydys–Witten equations on product manifolds $${M_5 = M_4 \times \mathbb{R}}$$M5=M4×R arise in the context of twisting the 5D maximally supersymmetric Yang–Mills theory. In this paper, we present the construction of twisted N = 2 Yang–Mills theory on Sasaki–Einstein manifolds, and more generally on K-contact manifolds. The localisation locus of this new theory thus provides a covariant version of the Haydys–Witten equation.
115164146
Odd Chern-Simons Theory, Lie Algebra Cohomology and Characteristic Classes
We investigate the generic 3D topological field theory within the AKSZ-BV framework. We use the Batalin-Vilkovisky (BV) formalism to construct explicitly cocycles of the Lie algebra of formal Hamiltonian vector fields and we argue that the perturbative partition function gives rise to secondary characteristic classes. We investigate a toy model which is an odd analogue of Chern-Simons theory, and we give some explicit computation of two point functions and show that its perturbation theory is identical to the Chern-Simons theory. We give a concrete example of the homomorphism taking Lie algebra cocycles to Q-characteristic classes, and we reinterpret the Rozansky-Witten model in this light.
56282767
The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere
A bstractBased on the construction by Hosomichi, Seong and Terashima we consider N = 1 supersymmetric 5D Yang-Mills theory with matter on a five-sphere with radius r. This theory can be thought of as a deformation of the theory in flat space with deformation parameter r and this deformation preserves 8 supercharges. We calculate the full perturbative partition function as a function of $ {{{r} \left/ {{g_Y^2}} \right.}_M} $, where $ {g_Y}_M $ is the Yang-Mills coupling, and the answer is given in terms of a matrix model. We perform the calculation using localization techniques. We also argue that in the large N-limit of this deformed 5D Yang-Mills theory this matrix model provides the leading contribution to the partition function and the rest is exponentially suppressed.
119130700
Quantization of Poisson Manifolds from the Integrability of the Modular Function
We discuss a framework for quantizing a Poisson manifold via the quantization of its symplectic groupoid, combining the tools of geometric quantization with the results of Renault’s theory of groupoid C*-algebras. This setting allows very singular polarizations. In particular, we consider the case when the modular function is multiplicatively integrable, i.e., when the space of leaves of the polarization inherits a groupoid structure. If suitable regularity conditions are satisfied, then one can define the quantum algebra as the convolution algebra of the subgroupoid of leaves satisfying the Bohr-Sommerfeld conditions.We apply this procedure to the case of a family of Poisson structures on $${\mathbb{C}P_n}$$CPn, seen as Poisson homogeneous spaces of the standard Poisson-Lie group SU(n + 1). We show that a bihamiltonian system on $${\mathbb{C}P_n}$$CPn defines a multiplicative integrable model on the symplectic groupoid; we compute the Bohr-Sommerfeld groupoid and show that it satisfies the needed properties for applying Renault theory. We recover and extend Sheu’s description of quantum homogeneous spaces as groupoid C*-algebras.
55165925
Wilson Lines from Representations of NQ-Manifolds
An NQ-manifold is a non-negatively graded supermanifold with a degree 1 homological vector field. The focus of this paper is to define the Wilson loops/lines in the context of NQ-manifolds and to study their properties. The Wilson loops/lines, which give the holonomy or parallel transport, are familiar objects in usual differential geometry, we analyze the subtleties in the generalization to the NQ-setting and we also sketch some possible applications of our construction.
115173241
2D and 3D topological field theories for generalized complex geometry
Using the Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) prescription we construct 2D and 3D topological field theories associated to generalized complex manifolds. These models can be thought of ...
49273245
Quark-gluon correlation functions relevant to single transverse spin asymmetries
We investigate the relative size of various twist-3 quark-gluon correlation functions relevant to single transverse spin asymmetries (SSAs) in a quark-diquark model of the nucleon. We calculate the quark-gluon correlation function T{sub q,F}(x,x) that is responsible for the gluonic pole contribution to the SSAs, as well as T{sub q,F}(0,x) and T{sub {Delta}q,F}(0,x) responsible for the fermionic pole contributions. We find in both cases of a scalar diquark and an axial-vector diquark that at the first nontrivial order only the T{sub q,F}(x,x) is finite while all other quark-gluon correlation functions vanish. Using the same model, we evaluate quark Sivers function and discuss its relation to the T{sub q,F}(x,x). We also discuss the implication of our finding to the phenomenological studies of the SSAs.
119169669
k{sub T} factorization is violated in production of high-transverse-momentum particles in hadron-hadron collisions
We show that hard-scattering factorization is violated in the production of high-p{sub T} hadrons in hadron-hadron collisions, in the case that the hadrons are back-to-back, so that k{sub T} factorization is to be used. The explicit counterexample that we construct is for the single-spin asymmetry with one beam transversely polarized. The Sivers function needed here has particular sensitivity to the Wilson lines in the parton densities. We use a greatly simplified model theory to make the breakdown of factorization easy to check explicitly. But the counterexample implies that standard arguments for factorization fail not just for the single-spin asymmetry but for the unpolarized cross section for back-to-back hadron production in QCD in hadron-hadron collisions. This is unlike corresponding cases in e{sup +}e{sup -} annihilation, Drell-Yan, and deeply inelastic scattering. Moreover, the result endangers factorization for more general hadroproduction processes.
24811462
QCD prediction for heavy boson transverse momentum distributions.
We investigate the predictive power of the Collins, Soper, and Sterman b-space QCD resummation formalism for transverse momentum ( Q(T)) distributions of heavy boson production in hadronic collisions. We show that the predictive power has a strong dependence on the collision energy sqrt[S] in addition to its well known Q2 dependence, and the sqrt[S] dependence improves the predictive power at collider energies. We demonstrate that, at the Fermilab Tevatron and the CERN LHC energies, the Q(T) distributions derived from b-space resummation are not sensitive to the nonperturbative input at large b, and give good descriptions of the Q(T) distributions of heavy boson production at all transverse momenta Q(T)< or =Q.
831153
Single transverse-spin asymmetry in the Drell-Yan lepton angular distribution
We calculate a single transverse-spin asymmetry for the Drell-Yan lepton-pair's angular distribution in perturbative QCD. At leading order in the strong coupling constant, the asymmetry is expressed in terms of a twist-3 quark-gluon correlation function T-F((V))(x(1), x(2)). In our calculation, the same result was obtained in both the light-cone and covariant gauges in QCD, while keeping explicit electromagnetic current conservation for the virtual photon that decays into the lepton pair. We also present a numerical estimate of the asymmetry and compare the result to another existing prediction.
10583946
Low-mass dilepton production in pp and AA collisions
Abstract We adopt a factorized QCD formalism to describe the transverse momentum distribution of lowmass lepton pairs produced in pp collisions, when the pair transverse momentum Q T 4 ≫ Q , with the pair's invariant mass Q as low as Q ∼ Λ Q C D . We extend this formalism to dilepton production in AA collisions by including the nuclear-dependent power correction due to parton multiple scattering.