119614535
Knot invariants and new weight systems from general 3D TFTs
Abstract We introduce and study the Wilson loops in general 3D topological field theories (TFTs), and show that the expectation value of Wilson loops also gives knot invariants as in the Chern–Simons theory. We study the TFTs within the Batalin–Vilkovisky (BV) and the Alexandrov–Kontsevich–Schwarz–Zaboronsky (AKSZ) framework, and the Ward identities of these theories imply that the expectation value of the Wilson loop is a pairing of two dual constructions of (co)cycles of certain extended graph complex (extended from Kontsevich’s graph complex to accommodate the Wilson loop). We also prove that there is an isomorphism between the same complex and certain extended Chevalley–Eilenberg complex of Hamiltonian vector fields. This isomorphism allows us to generalize the Lie algebra weight system for knots to weight systems associated with any homological vector field and its representations. As an example we construct knot invariants using holomorphic vector bundle over hyperKahler manifolds.
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 ...
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.
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.
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.
116908028
Knot Weight Systems from Graded Symplectic Geometry
We show that from an even degree symplectic NQ-manifold, whose homological vector field Q preserves the symplectic form, one can construct a weight system for tri-valent graphs with values in the Q-cohomology ring, satisfying the IHX relation. Likewise, given a representation of the homological vector field, one can construct a weight system for the chord diagrams, satisfying the IHX and STU relations. Moreover we show that the use of the 'Gronthendieck connection' in the construction is essential in making the weight system dependent only on the choice of the NQ-manifold and its representation.
13483939
Resummed QCD power corrections to nuclear shadowing.
We calculate and resum a perturbative expansion of nuclear enhanced power corrections to the structure functions measured in deeply inelastic scattering of leptons on a nuclear target. Our results for the Bjorken x, Q2 and A dependence of nuclear shadowing in F2A(x,Q2) and the nuclear modification to FAL(x,Q2), obtained in terms of the QCD factorization approach, are consistent with the existing data. We demonstrate that the low Q2 behavior of these data and the measured large longitudinal structure function point to a critical role for the power corrections when compared to other theoretical approaches.
119444624
Single transverse-spin asymmetry in high transverse momentum pion production in pp collisions
We study the single-spin (left-right) asymmetry in single-inclusive pion production in hadronic scattering. This asymmetry is power-suppressed in the transverse momentum of the produced pion and can be analyzed in terms of twist-three parton correlation functions in the proton. We present new calculations of the corresponding partonic hard-scattering functions that include the so-called ``nonderivative'' contributions not previously considered in the literature. We find a remarkably simple structure of the results. We also present a brief phenomenological study of the spin asymmetry, taking into account data from fixed-target scattering and also the latest information available from Relativistic Heavy Ion Collider (RHIC). We make additional predictions that may be tested experimentally at RHIC.
118646218
Color-transfer enhancement for heavy quarkonium production
We study the transfer of color between a heavy quark pair and an unpaired heavy quark or antiquark moving at a nonrelativistic velocity with respect to the pair. We find that the open heavy quark or antiquark can catalyze the transformation of the pair from octet representation at short distances to singlet at long distances. This process is infrared sensitive in general, and we exhibit double poles in dimensional regularization at next-to-next-to-leading order in the transition probability. Because of their dependence on kinematic variables, these poles cannot be matched to the nonperturbative matrix elements of effective field theories based on a single heavy quark pair.
119390410
Nuclear shadowing in neutrino–nucleus deeply inelastic scattering
Abstract In the framework of the collinear factorized pQCD approach we calculate the small-xB process-dependent nuclear modification to the structure functions measured in neutrino–nucleus deeply inelastic scattering. We include both heavy quark mass corrections (M2/Q2) and resummed nuclear-enhanced dynamical power corrections in the quantity (ξ2/Q2)(A1/3−1) with ξ2 evaluated to leading order in αs. Our formalism predicts a measurable difference in the shadowing pattern of the structure functions F2A(xB,Q2) and F3A(xB,Q2) and a significant low- and moderate-Q2 modification of the QCD sum rules. We also comment on the relevance of our results to the NuTeV extraction of sin2θW.
8258813
Color transfer in associated heavy-quarkonium production.
We study the production of heavy quarkonium in association with an additional heavy pair. We argue that important contributions may come from phase space regions where three heavy fermions are separated by relative velocities much lower than the speed of light, and to which standard effective field theories do not apply. In this region, infrared sensitive color exchange is specific to the presence of the unpaired (anti)quark. This effect vanishes as the motion of the additional particle becomes relativistic with respect to the pair, and is completely absent for massless quarks and gluons in the final state.