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.
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 ...
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.
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.
59473327
Introduction to Graded Geometry, Batalin-Vilkovisky Formalism and their Applications
These notes are intended to provide a self-contained introduction to the basic ideas of finite dimensional Batalin-Vilkovisky (BV) formalism and its applications. A brief exposition of super- and graded geometries is also given. The BV-formalism is introduced through an odd Fourier transform and the algebraic aspects of integration theory are stressed. As a main application we consider the perturbation theory for certain finite dimensional integrals within BV-formalism. As an illustration we present a proof of the isomorphism between the graph complex and the Chevalley-Eilenberg complex of formal Hamiltonian vectors fields. We briefly discuss how these ideas can be extended to the infinite dimensional setting. These notes should be accessible to both physicists and mathematicians.
15055597
Dimensional regularization and dimensional reduction in the light cone
We calculate all of the 2 to 2 scattering process in Yang-Mills theory in the light cone gauge, with the dimensional regulator as the UV regulator. The IR is regulated with a cutoff in ${q}^{+}$. It supplements our earlier work, where a Lorentz noncovariant regulator was used, and the final results bear some problems in gauge fixing. Supersymmetry relations among various amplitudes are checked by using the light cone superfields.
119231626
Low-mass lepton pair production at large transverse momentum
We study the transverse momentum distribution of low-mass lepton pairs produced in hadronic scattering, using the perturbative QCD factorization approach. We argue that the distribution at large transverse momentum, Q{sub T}>>Q, with the pair's invariant mass Q as low as Q{approx}{lambda}{sub QCD}, can be systematically factorized into universal parton-to-lepton pair fragmentation functions, parton distributions, and perturbatively calculable partonic hard parts evaluated at a short-distance scale {approx}O(1/Q{sub T}). We introduce a model for the input lepton pair fragmentation functions at a scale {mu}{sub 0}{approx}1 GeV, which are then evolved perturbatively to scales relevant at the Relativistic Heavy Ion Collider. Using the evolved fragmentation functions, we calculate the transverse momentum distributions in hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions at the Relativistic Heavy Ion Collider. We also discuss the sensitivity of the transverse momentum distribution of low-mass lepton pairs to the gluon distribution.
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.
119690878
Asymmetric di-jet production in polarized hadronic collisions
Abstract Using the collinear QCD factorization approach, we study the single-transverse-spin dependent cross section Δ σ ( S ⊥ ) for the hadronic production of two jets of momenta P 1 = P + q / 2 and P 2 = − P + q / 2 . We consider the kinematic region where the transverse components of the momentum vectors satisfy P ⊥ ≫ q ⊥ ≫ Λ QCD . For the case of initial-state gluon radiation, we show that at the leading power in q ⊥ / P ⊥ and at the lowest non-trivial perturbative order, the dependence of Δ σ ( S ⊥ ) on q ⊥ decouples from that on P ⊥ , so that the cross section can be factorized into a hard part that is a function only of the single scale P ⊥ , and into perturbatively generated transverse-momentum dependent (TMD) parton distributions with transverse momenta k ⊥ = O ( q ⊥ ) .
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.
118752418
High twist effects in hadronic collisions
We analyze the first nonleading power corrections to inclusive hadron‐hadron scattering cross sections. Such corrections decrease as 1/Q relative to leading power in the case of polarized hadronic collisions, or as 1/Q2 in the case of unpolarized hadronic collisions. We show why such corrections may be treated in perturbative QCD, in terms of generalized factorization theorems.