118672738
From spin vertex to string vertex
A bstractIn the recent publication [1] the spin vertex was introduced as a new approach for computing three-point functions in N=4$$ \mathcal{N}=4 $$ SYM. In this note we consider the BMN limit of the spin vertex for scalar excitations and show that it reproduces the string vertex in the light-cone string field theory which describes the string interactions in the pp-wave background at the leading order of λ′ expansion. This is achieved by introducing a polynomial representation for the spin vertex. We derive the Neumann coefficients from the spin vertex at weak coupling and show they match with the Neumann coefficients from the string field theory.
4807800
Fixing the quantum three-point function
A bstractWe propose a new method for the computation of quantum three-point functions for operators in $ \mathfrak{s}\mathfrak{u} $(2) sectors of $ \mathcal{N} $ = 4 super Yang-Mills theory. The method is based on the existence of a unitary transformation relating inhomogeneous and long-range spin chains. This transformation can be traced back to a combination of boost operators and an inhomogeneous version of Baxter’s corner transfer matrix. We reproduce the existing results for the one-loop structure constants in a simplified form and indicate how to use the method at higher loop orders. Then we evaluate the one-loop structure constants in the quasiclassical limit and compare them with the recent strong coupling computation.
118460136
The Crepant Transformation Conjecture for Toric Complete Intersections
Abstract Let X and Y be K -equivalent toric Deligne–Mumford stacks related by a single toric wall-crossing. We prove the Crepant Transformation Conjecture in this case, fully-equivariantly and in genus zero. That is, we show that the equivariant quantum connections for X and Y become gauge-equivalent after analytic continuation in quantum parameters. Furthermore we identify the gauge transformation involved, which can be thought of as a linear symplectomorphism between the Givental spaces for X and Y , with a Fourier–Mukai transformation between the K -groups of X and Y , via an equivariant version of the Gamma-integral structure on quantum cohomology. We prove similar results for toric complete intersections. We impose only very weak geometric hypotheses on X and Y : they can be non-compact, for example, and need not be weak Fano or have Gorenstein coarse moduli space. Our main tools are the Mirror Theorems for toric Deligne–Mumford stacks and toric complete intersections, and the Mellin–Barnes method for analytic continuation of hypergeometric functions.
118329440
Virtual signed Euler characteristics
Roughly speaking, to any space $M$ with perfect obstruction theory we associate a space $N$ with symmetric perfect obstruction theory. It is a cone over $M$ given by the dual of the obstruction sheaf of $M$, and contains $M$ as its zero section. It is locally the critical locus of a function. 
More precisely, in the language of derived algebraic geometry, to any quasi-smooth space $M$ we associate its $(-1)$-shifted cotangent bundle $N$. 
By localising from $N$ to its $\mathbb C^*$-fixed locus $M$ this gives five notions of virtual signed Euler characteristic of $M$: 
(1) The Ciocan-Fontanine-Kapranov/Fantechi-G\"ottsche signed virtual Euler characteristic of $M$ defined using its own obstruction theory, 
(2) Graber-Pandharipande's virtual Atiyah-Bott localisation of the virtual cycle of $N$ to $M$, 
(3) Behrend's Kai-weighted Euler characteristic localisation of the virtual cycle of $N$ to $M$, 
(4) Kiem-Li's cosection localisation of the virtual cycle of $N$ to $M$, 
(5) $(-1)^{vd}$ times by the topological Euler characteristic of $M$. 
Our main result is that (1)=(2) and (3)=(4)=(5). The first two are deformation invariant while the last three are not.
124816809
Toric sheaves on weighted projective planes
We give an explicit description of toric sheaves on the weighted projective plane P(a, b, c) viewed as a toric Deligne-Mumford stack. The stack P(a, b, c) has an action of the torus T = C and by a toric sheaf we mean a coherent sheaf together with a lift of the torus action. The integers (a, b, c) are not necessarily chosen coprime or mutually coprime allowing for gerbe and root stack structures. This is a first step in an attempt to give an explicit description of toric sheaves on any smooth toric Deligne-Mumford stack. Specializing the description to torsion free sheaves gives a combinatorial picture with various new features, which do not appear in the case of smooth toric varieties. As an application, we describe the fixed point locus of the moduli scheme of stable rank 1 and 2 torsion free sheaves on P(a, b, c) with fixed K-group class. Summing over all K-group classes, we obtain formulae for generating functions of the topological Euler characteristics of these moduli schemes.
53533731
String bits and the spin vertex
Abstract We initiate a novel formalism for computing correlation functions of trace operators in the planar N = 4 SYM theory. The central object in our formalism is the spin vertex which is the weak coupling analogy of the string vertex in string field theory. We construct the spin vertex explicitly for all sectors at the leading order using a set of bosonic and fermionic oscillators. We prove that the vertex has trivial monodromy, or put in other words, it is a Yangian invariant. Since the monodromy of the vertex is the product of the monodromies of the three states, the Yangian invariance of the vertex implies an infinite exact symmetry for the three-point function. We conjecture that this infinite symmetry can be lifted to any loop order.
119302026
The quark number susceptibility in the hard-thermal-loop approximation
With the help of the vector Ward–Takahashi identity we derive a general formula for the quark number susceptibility (QNS) which expresses the QNS as an integral expression only involving the full quark propagator at finite temperature and chemical potential. The QNS at finite temperature and zero chemical potential is calculated with the dressed quark propagator in the hard-thermal-loop (HTL) approximation. A comparison of our result with the results of the QNS in the HTL approximation in previous literatures is given.
120218128
Time-dependent harmonic oscillator in a magnetic field and an electric field on the non-commutative plane
In the non-commutative space, wave functions and geometric phases are derived for the time-dependent harmonic oscillator in external time-dependent magnetic and electric field. Explicit forms of the coherent states are also given, which are not the minimum uncertainty states for the coordinates and momenta.
121809939
The Wigner solution of quark gap equation and chiral phase transition of QCD at finite temperature and nonzero chemical potential
By employing some modification to the normal NJL model, we discuss the Wigner solution of quark gap equation at finite temperature and chemical potential when the current quark mass m is nonzero. The discovery of the coexistence of the Nambu solution and the Wigner solution at finite temperature and chemical potential beyond the chiral limit is of great importance in the study of the chiral phase transition of QCD. Using the pressure difference between Nambu phase and Wigner phase (or in other words, the bag constant) as an order parameter for chiral phase transition, we draw a possible phase diagram based on our calculations.
118727713
INFLUENCE OF A UNIFORM MAGNETIC FIELD ON DYNAMICAL CHIRAL SYMMETRY BREAKING IN QED3
We study dynamical chiral symmetry breaking (DCSB) in an effective QED3 theory of d-wave high temperature cuprate superconductors under a uniform magnetic field. At zero temperature, the external magnetic field induces a mixed state by generating vortices in the condensate of charged holons. The growing magnetic field suppresses the superfluid density and thus reduces the gauge field mass which is opened via the Anderson–Higgs mechanism. By numerically solving the Dyson–Schwinger gap equation, we show that the massless fermions acquires a dynamical gap through DCSB mechanism when the magnetic field strength H is above a critical value Hc and the fermion flavors N is below a critical value Nc. Further, it is found that both Nc and the dynamical fermion gap increase as the magnetic field H grows. It is expected that our result can be tested in phenomena in high temperature cuprate superconductors.
118596846
The constrained NMSSM and Higgs near 125 GeV
Abstract We assess the extent to which various constrained versions of the NMSSM are able to describe the recent hints of a Higgs signal at the LHC corresponding to a Higgs mass in the range 123–128 GeV.