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.
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.
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.
118172840
Search for the electron electric dipole moment
Extensions to the Standard Model (SM) typically include new heavy particles and new mechanisms for CP violation. These underlying phenomena can give rise to electric dipole moments of the electron and other particles. Tabletop‐scale experiments used to search for these effects are described. Present experiments are already sensitive to new physics at the TeV scale, and new methods could extend this range dramatically. Such experiments could be among the first to show evidence for physics beyond the SM.
119275366
125 GeV Higgs bosons in two-Higgs-doublet models
Moriond 2013 ALTAS data at 125 GeV state appears to exhibit a substantial excess in the di-photon final state and in the ZZ decaying to four lepton channel, whereas which are more or less SM-like rate observed by CMS MVA analysis. We examine the maximum Higgs signal enhancements that can be achieved in the 2HDM when either a single Higgs or more than one Higgs have mass(es) near 125 GeV. In general, the constraints of vacuum stability, unitarity and perturbativity play the key role in restricting possibilities of signal enhancement. The Type II model allows for an enhancement in the di-photon rate (relative to the SM) of the order of 2-3 but associated with an even larger ZZ or too large \tau\tau signal. In contrast, the maximal value of the di-photon signal in the Type I model can reach the order of 1.3 for which the ZZ signal is of order 1.
118135921
Two Higgs Bosons at the Tevatron and the LHC
The best fit to the Tevatron results in the bb channel and the mild excesses at CMS in the gamma-gamma channel at 136 GeV and in the tau-tau channel above 132 GeV can be explained by a second Higgs state in this mass range, in addition to the one at 125 GeV recently discovered at the LHC. We show that a scenario with two Higgs bosons at 125 GeV and 136 GeV can be consistent with practically all available signal rates, including a reduced rate in the tau-tau channel around 125 GeV as reported by CMS. An example in the parameter space of the general NMSSM is given where, moreover, the signal rates of the 125 GeV Higgs boson in the gamma-gamma channels are enhanced relative to the expectation for a SM Higgs boson of this mass.
118998757
Constraints on and future prospects for Two-Higgs-Doublet Models in light of the LHC Higgs signal
We analyze the Two-Higgs-Doublet Models (2HDMs) of Type I and II for consistency with the latest measurements of the ~125.5 GeV Higgs-like signal at the LHC. To this end, we perform scans of the 2HDM parameter space taking into account all relevant pre-LHC constraints as well as the most recent limits coming from searches for heavy Higgs-like states at the LHC. The current status of the 2HDMs of Type I and II is discussed assuming that the observed 125.5 GeV state is one of the two CP-even Higgs bosons, either the lighter h or the heavier H. Implications for future experiments, including expectations regarding other lighter or heavier Higgs bosons are given. The possible importance of heavier Higgs bosons feeding the signals for the 125.5 GeV state is also evaluated.
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.