119317778
Gopakumar-Vafa BPS invariants, Hilbert schemes and quasimodular forms. I
We prove a closed formula for leading Gopakumar- Vafa BPS invariants of local Calabi-Yau geometries given by the canonical line bundles of toric Fano surfaces. It shares some sim- ilar features with Gottsche-Yau-Zaslow formula: Connection with Hilbert schemes, connection with quasimodular forms, and qua- dratic property after suitable transformation. In Part I of this paper we will present the case of projective plane, more general cases will be presented in Part II. The problem of counting curves in algebraic varieties dates back to the nineteenth century. Classical examples include the famous 27 lines on a cubic surface and the 2875 lines on a quintic 3-fold. Through the interaction with string theory, spectacular progresses in this classi- cal branch of algebraic geometry have been made over the years since 1990's. First of all, Gromov-Witten theory and its various variants have laid the foundation for the modern treatment of many classical enumerative problems and greatly expanded the range of enumerative problems being considered. See (PT) for an introduction to some of the exciting developments. The study of the problems of counting curves in surfaces and Calabi- Yau 3-folds have served both as motivations and applications of Gromov- Witten theory. We will recall some results in these directions in §2 and §3 to serve as motivations for this work. We emphasize on the following three salient features for the curving counting problems for algebraic surfaces: connection with Hilbert schemes, connection with quasimod- ular forms, and quadratic properties of the node polynomials after suit- able transformation. Our main results will show that these features are also shared in the curve counting problems of some noncompact Calabi- Yau 3-folds, arising as the the total space of the canonical line bundles of toric Fano surfaces. 1
119173691
Some integrality properties in local mirror symmetry
We prove some integrality properties of the open-closed mirror maps, inverse open-closed mirror maps and mirror curves of some local Calabi-Yau geometries.
18702885
Curve counting and instanton counting
We prove some combinatorial results required for the proof of the following conjecture of Nekrasov: The generating function of closed string invariants in local Calabi-Yau geometries obtained by appropriate fibrations of $A_N$ singularities over $P^1$ reproduce the generating function of equivariant $\hat{A}$-genera of moduli space of instants on $C^2$.
119648995
On fermionic representation of the framed topological vertex
A bstractThe Gromov-Witten invariants of ℂ3$$ {\mathbb{C}}^3 $$ with branes is encoded in the topological vertex which has a very complicated combinatorial expression. A simple formula for the topological vertex was proposed by Aganagic et al. in the fermionic picture. We will propose a similar formula for the framed topological vertex and prove it in the case when there are one or two branes.
2897011
A formula of two-partition Hodge integrals
JMg,n where tpi = ci(L?) is the first Chern class of L?, and Xj = Cj(E) is the j-th Chern class of the Hodge bundle. The study of Hodge integrals is an important part of intersection theory on Mg,n> Hodge integrals also naturally arise when one computes Gromov-Witten invariants by localization techniques. For example, the following generating series of Hodge integrals arises when one computes local invariants of a toric Fano surface in a Calabi-Yau 3-fold by virtual localization [33]:
8970059
On a Proof of a Conjecture of Marino-Vafa on Hodge Integrals
We prove a remarkable formula for Hodge integrals conjectured by Marino and Vafa based on large N duality, using functorial virtual localization on certain moduli spaces of relative stable morphisms.
119260156
Higgs boson production in high energy proton-nucleus collisions
AbstractWe study Higgs boson production from gluon-gluon fusion at mid-rapidity in high energy proton-nucleuscollisions.Forthisprocessthe presentlystilllittle knowngluondistributionfunction h ⊥g1 (x,k ⊥ )might give a numerically relevant contribution. We show by explicite calculation that using CGC(color glass condensate) model input the result obtained in the naive k t factorization approachmatches the result obtained in the TMD factorization framework for a dilute medium. We also ver-ify the earlier ﬁnding [14] that the k t factorization formalism for Higgs production breaks down ina dense medium. In doing so we formulate a hybrid model which allows one to treat such reactionstheoretically. 1 Introduction In recent years the theoretical understanding of transverse momentum dependent (TMD) partondistributions has made tremendous progress, up to the point that their further investigation can serveas one of the motivations for a new electron-ion collider [1]. Still there are many aspects which needfurther study. An especially interesting one is relevant for Higgs-production at the LHC. In thiscase it was realized that for pp collisions in addition to the standard gluon contribution one gets acontribution proportional to a little known distribution function, usually refereed to as the distributionof linearly polarized gluons [2,3] (h
17657545
Multiple parton scattering in nuclei: gauge invariance
Within the framework of a generalized collinear factorization for multiple parton scattering in nuclear medium, twist-4 contributions to DIS off a large nucleus can be factorized as a convolution of hard parts and two-parton correlation functions. The hard parts for the quark scattering in the light-cone gauge correspond to interaction with a transverse (physical) gluon in the target, while they are given by the second derivative of the cross section with a longitudinal gluon in the covariant gauge. We provide a general proof of the equivalence of the hard parts in the light-cone and covariant gauge. We further demonstrate the equivalence in calculations of twist-4 contributions to semi-inclusive cross section of DIS in both lowest order and next leading order. Calculations of the nuclear transverse momentum broadening of the struck quark in the light-cone and covariant gauge are also discussed.
53325191
Distribution of linearly polarized gluons inside a large nucleus
The distribution of linearly polarized gluons inside a large nucleus is studied in the framework of the color glass condensate. We find that the Weizsacker-Williams distribution saturates the positivity bound at large transverse momenta and is suppressed at small transverse momenta, whereas the dipole distribution saturates the bound for any value of the transverse momentum. We also discuss processes in which both distributions of linearly polarized gluons can be probed.
117468519
Transverse momentum dependent quark distributions and polarized Drell-Yan processes
We study the spin-dependent quark distributions at large transverse momentum. We derive their transverse momentum behaviors in the collinear factorization approach in this region. We further calculate the angular distribution of the Drell-Yan lepton pair production with polarized beams and present the results in terms of the collinear twist-three quark-gluon correlation functions. In the intermediate transverse momentum region, we find that the two pproaches: the collinear factorization and the transverse momentum dependent factorization approaches are consistent in the description of the lepton pair angular distributions.
119690858
SINGLE SPIN ASYMMETRIES IN INCLUSIVE DIS AND MULTI-PARTON CORRELATIONS IN THE NUCLEON
Transverse single spin asymmetries in inclusive deep-inelastic lepton-nucleon scattering can be generated through multi-photon exchange between the leptonic and the hadronic part of the process. Here we consider two-photon exchange, and mainly focus on the transverse target spin asymmetry. In particular, we investigate the case where two photons couple to different quarks. Such a contribution involves a quark-photon-quark correlator in the nucleon, which has a (model-dependent) relation to the Efremov-Teryaev-Qiu-Sterman quark-gluon-quark correlator TF. Using different parameterizations for TF we compute the transverse target spin asymmetry for both a proton and a neutron target, and compare the results to recent experimental data. Potential implications on our general understanding of single spin asymmetries in hard scattering processes are discussed as well.