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.
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.
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 ...
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.
15737254
On the AKSZ formulation of the Rozansky-Witten theory and beyond
Using the AKSZ formalism, we construct the Batalin-Vilkovisky master action for the Rozansky-Witten model, which can be defined for any complex manifold with a closed (2,0)-form. We also construct the holomorphic version of Rozansky-Witten theory defined over Calabi-Yau 3-fold.
15941815
Single transverse-spin asymmetries in hadronic pion production
We analyze single transverse-spin asymmetries for hadronic pion production at large transverse momenta using QCD factorization. In the large ${x}_{F}$ region, leading contributions to the asymmetries are naturally produced by twist-3 parton correlation functions that couple quark fields and gluon field strengths. With a simple model for these matrix elements, leading-order asymmetries calculated from QCD are consistent with data on pion production from Fermilab, and can be used to predict single-spin asymmetries at BNL RHIC. We argue that our perturbative calculation for the asymmetries is relevant to pion transverse momenta as low as a few GeV.
119631335
Nuclear Shadowing at Small Values of x
The nuclear parton distributions are given in a model where the nucleus is viewed as a collection of uncorrelated nucleons. Using these distributions, we determine nuclear shadowing at small values of x. We find that the effect of nuclear shadowing goes away very slowly when Q2 increases. Our results are consistent with the experiment of Goodman et al. The amount of nuclear shadowing expected at higher energies is discussed.
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.
14549658
COHERENT MULTIPLE SCATTERING AND DIHADRON CORRELATIONS IN HEAVY ION COLLISIONS
We present a systematic calculation of the coherent multiple parton scattering with several nucleons in lepton-nucleus and hadron-nucleus collisions. We show that in l+A reactions coherence leads to nuclear shadowing in the structure functions and a modification of the QCD sum rules. In p+A reactions we evaluate the nuclear suppression of single and double inclusive hadron production at moderate transverse momenta. We demonstrate that both spectra and dihadron correlations in p+A collisions at RHIC are sensitive measures of such dynamical nuclear attenuation effects.
119435335
Summary of Spin Physics Parallel Sessions
We summarize the activities in the spin physics parallel sessions of the 8th conference on intersections between particle and nuclear physics.