Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds

We present a proof of the mirror conjecture of Aganagic and Vafa (Mirror Symmetry, D-Branes and Counting Holomorphic Discs. http://arxiv.org/abs/hep-th/0012041v1, 2000) and Aganagic et al. (Z Naturforsch A 57(1–2):128, 2002) on disk enumeration in toric Calabi-Yau 3-folds for all smooth semi-projective toric Calabi-Yau 3-folds. We consider both inner and outer branes, at arbitrary framing. In particular, we recover previous results on the conjecture for (i) an inner brane at zero framing in ${K_{\mathbb{P}^2}}$ K P 2 (Graber-Zaslow, Contemp Math 310:107–121, 2002), (ii) an outer brane at arbitrary framing in the resolved conifold ${\mathcal{O}_{\mathbb{P}^1}(-1)\oplus \mathcal{O}_{\mathbb{P}^1}(-1)}$ O P 1 ( - 1 ) ⊕ O P 1 ( - 1 ) (Zhou, Open string invariants and mirror curve of the resolved conifold. http://arxiv.org/abs/1001.0447v1 [math.AG], 2010), and (iii) an outer brane at zero framing in ${K_{\mathbb{P}^2}}$ K P 2 (Brini, Open topological strings and integrable hierarchies: Remodeling the A-model. http://arxiv.org/abs/1102.0281 [hep-th], 2011).     

Decoherent Histories of Spin Networks

The decoherent histories formalism, developed by Griffiths, Gell-Mann, and Hartle (in Phys. Rev. A 76:022104, 2007; arXiv:1106.0767v3 [quant-ph], 2011; Consistent Quantum Theory, Cambridge University Press, 2003; arXiv:gr-qc/9304006v2, 1992) is a general framework in which to formulate a timeless, ‘generalised’ quantum theory and extract predictions from it. Recent advances in spin foam models allow for loop gravity to be cast in this framework. In this paper, I propose a decoherence functional for loop gravity and interpret existing results (Bianchi et al. in Phys. Rev. D 83:104015, 2011; Phys. Rev. D 82:084035, 2010) as showing that coarse grained histories follow quasiclassical trajectories in the appropriate limit.     

Log-Gamma Polymer Free Energy Fluctuations via a Fredholm Determinant Identity

We prove that under n ^1/3 scaling, the limiting distribution as n → ∞ of the free energy of Seppäläinen’s log-Gamma discrete directed polymer is GUE Tracy-Widom. The main technical innovation we provide is a general identity between a class of n-fold contour integrals and a class of Fredholm determinants. Applying this identity to the integral formula proved in Corwin et al. (Tropical combinatorics and Whittaker functions. http://arxiv.org/abs/1110.3489v3 [math.PR], 2012) for the Laplace transform of the log-Gamma polymer partition function, we arrive at a Fredholm determinant which lends itself to asymptotic analysis (and thus yields the free energy limit theorem). The Fredholm determinant was anticipated in Borodin and Corwin (Macdonald processes. http://arxiv.org/abs/1111.4408v3 [math.PR], 2012) via the formalism of Macdonald processes yet its rigorous proof was so far lacking because of the nontriviality of certain decay estimates required by that approach.     

The Parafermionic Observable in SLE

The parafermionic observable has recently been used by number of authors to study discrete models, believed to be conformally invariant and to prove convergence results for these processes to SLE (Beffara and Duminil-Copin in arXiv:1010.0526v2, 2011; Duminil-Copin and Smirnov in arXiv:1007.0575v2, 2011; Hongler and Smirnov in arXiv:1008.2645v3, 2011; Ikhlef and Cardy in J. Phys. A 42:102001, 2009; Lawler in preprint, 2011; Rajabpour and Cardy in J. Phys. A 40:14703, 2007; Riva and Cardy in J. Stat. Mech. Theory Exp., 2006; Smirnov in International Congress of Mathematicians, vol. II, pp. 1421?C1451, 2006; Smirnov in Ann. Math. 172(2):1435?C1467, 2010; Smirnov in Proceedings of the International Congress of Mathematicians, Hyderabad 2010, vol.?I, pp. 595?C621, 2010). We provide a definition for a one parameter family of continuum versions of the parafermionic observable for SLE, which takes the form of a normalized limit of expressions identical to the discrete definition. We then show the limit defining the observable exists, compute the value of the observable up to a finite multiplicative constant, and prove this constant is non-zero for a wide range of ??. Finally, we show our observable for SLE becomes a holomorphic function for a particular choice of the parameter, which provides a new point of view on a fundamental property of the discrete observable.     

Operational Independence and Operational Separability in Algebraic Quantum Mechanics

Recently, new types of independence of a pair of C ^*- or W ^*-subalgebras $({\mathcal{A}}_{1},{\mathcal{A}}_{2})$ of a C ^*- or W ^*-algebra have been introduced: operational C ^*- and W ^*-independence (Rédei and Summers, http://arxiv.org/abs/0810.5294, 2008) and operational C ^*- and W ^*-separability (Rédei and Valente, How local are local operations in local quantum field theory? 2009). In this paper it is shown that operational C ^*-independence is equivalent to operational C ^*-separability and that operational W ^*-independence is equivalent to operational W ^*-separability. Specific further sub-types of both operational C ^*- and W ^*-separability and operational C ^*- and W ^*-independence are defined and the problem of characterization of the logical interdependencies of the independence notions is raised.     

Tunneling and Metastability of Continuous Time Markov Chains II, the Nonreversible Case

We proposed in Beltrán and Landim (J.?Stat. Phys. 140:1065?C1114, 2010) a new approach to prove the metastable behavior of reversible dynamics based on potential theory and local ergodicity. In this article we extend this theory to nonreversible dynamics based on the Dirichlet principle proved in Gaudillière and Landim (arXiv:1111.2445, 2011). We?also include in this article the proof of the metastability of a class of birth and death chains.     

Viability of Noether Symmetry of F(R) Theory of Gravity

Recently, we have explored vices and virtues of $R^{\frac{3}{2}}$ term in the action which has in-built Noether symmetry and anticipated that a linear term might improve the situation (Sarkar et al., arXiv:1201.2987 [astro-ph.CO], 2012). In the absence of a conserved current it is extremely difficult to obtain an analytical solution of the said fourth order theory of gravity in the presence of a linear term. Here, we therefore enlarge the configuration space by including a scalar field in addition and also taking some of the anisotropic models (in the absence of a scalar field) into account. We observe that Noether symmetry remains obscure and it does not even reproduce the one that already exists in the literature (Sanyal, Gen. Relativ. Gravit., 37:407, 2005). However, there exists in general, a conserved current for F(R) theory of gravity in the presence of a non-minimally coupled scalar field (Sanyal, Phys. Lett. B, 624:81, 2005; Mod. Phys. Lett. A, 25:2667, 2010), which simplifies the field equations considerably. Here, we briefly expatiate the non-Noether conserved current and show that indeed the situation is modified.     

Asymptotics of a Discrete-Time Particle System Near a Reflecting Boundary

We examine a discrete-time Markovian particle system on ?×?₊ introduced in Defosseux (arXiv:1012.0117v1). The boundary {0}×?₊ acts as a reflecting wall. The particle system lies in the Anisotropic Kardar-Parisi-Zhang with a wall universality class. After projecting to a single horizontal level, we take the long-time asymptotics and obtain the discrete Jacobi and symmetric Pearcey kernels. This is achieved by showing that the particle system is identical to a Markov chain arising from representations of O(∞) (introduced in Borodin and Kuan (Commun. Pure. Appl. Math. 63(7):831–894, 2010, arXiv:0904.2607)). The fixed-time marginals of this Markov chain are known to be determinantal point processes, allowing us to take the limit of the correlation kernel. We also give a simple example which shows that in the multi-level case, the particle system and the Markov chain evolve differently.     

Probing compositeness with Higgs Boson decays at the LHC

We study how massive ghost-free gravity \(f(R)\) -modified theories, MGFTs, can be encoded into generic off-diagonal Einstein spaces. Using “auxiliary” connections completely defined by the metric fields and adapted to nonholonomic frames with associated nonlinear connection structure, we decouple and integrate in certain general forms the field equations in MGFT. Imposing additional nonholonomic constraints, we can generate Levi-Civita, LC, configurations and mimic MGFT effects via off-diagonal interactions of effective Einstein and/or Einstein–Cartan gravity with nonholonomically induced torsion. We show that imposing nonholonomic constraints it is possible reproduce very specific models of massive \(f(R)\) gravity studied in Cai et al. (arXiv:1307.7150, 2013), Klusoňet al. (Phys Lett B 726:918, 2013), Nojiri and Odintov (Phys Lett B 716:377, 2012) and Nojiri et al. (JCAP 1305:020, 2013). The cosmological evolution of ghost-free off-diagonal Einstein spaces is investigated. Certain compatibility of MGFT cosmology to small off-diagonal deformations of \(\Lambda \) CDM models is established.     

Quantum Correlations and the Measurement Problem

The transition from classical to quantum mechanics rests on the recognition that the structure of information is not what we thought it was: there are operational, i.e., phenomenal, probabilistic correlations that lie outside the polytope of local correlations. Such correlations cannot be simulated with classical resources, which generate classical correlations represented by the points in a simplex, where the vertices of the simplex represent joint deterministic states that are the common causes of the correlations. The ‘no go’ hidden variable theorems tell us that we can’t shoe-horn phenomenal correlations outside the local polytope into a classical simplex by supposing that something has been left out of the story. The replacement of the classical simplex by the quantum convex set as the structure representing probabilistic correlations is the analogue for quantum mechanics of the replacement of Newton’s Euclidean space and time by Minkowski spacetime in special relativity. The nonclassical features of quantum mechanics, including the irreducible information loss on measurement, are generic features of correlations that lie outside the classical simplex. This paper is an elaboration of these ideas, which have their source in work by Pitowsky (J. Math. Phys. 27:1556, 1986; Math. Program. 50:395, 1991; Phys. Rev. A 77:062109, 2008), Garg and Mermin (Found. Phys. 14:1–39, 1984), Barrett (Phys. Rev. A 75:032304, 2007; Phys. Rev. A 7:022101, 2005) and others, e.g., Brunner et al. (arXiv:1303.2849, 2013), but the literature goes back to Boole (An Investigation of the Laws of Thought, Dover, New York, 1951). The final section looks at the measurement problem of quantum mechanics in this context. A large part of the problem is removed by seeing that the inconsistency in reconciling the entangled state at the end of a quantum measurement process with the definiteness of the macroscopic pointer reading and the definiteness of the correlated value of the measured micro-observable depends on a stipulation that is not required by the structure of the quantum possibility space. Replacing this stipulation by an alternative consistent stipulation is the first step to resolving the problem.     

The Hamiltonian of Einstein affine-metric formulation of General Relativity

It is shown that the Hamiltonian of the Einstein affine-metric (first-order) formulation of General Relativity (GR) leads to a constraint structure that allows the restoration of its unique gauge invariance, four-diffeomorphism, without the need of any field dependent redefinition of gauge parameters as in the case of the second-order formulation. In the second-order formulation of ADM gravity the need for such a redefinition is the result of the non-canonical change of variables (arXiv:0809.0097). For the first-order formulation, the necessity of such a redefinition “to correspond to diffeomorphism invariance” (reported by Ghalati, arXiv:0901.3344) is just an artifact of using the Henneaux–Teitelboim–Zanelli ansatz (Nucl. Phys. B 332:169, 1990), which is sensitive to the choice of linear combination of tertiary constraints. This ansatz cannot be used as an algorithm for finding a gauge invariance, which is a unique property of a physical system, and it should not be affected by different choices of linear combinations of non-primary first class constraints. The algorithm of Castellani (Ann. Phys. 143:357, 1982) is free from such a deficiency and it leads directly to four-diffeomorphism invariance for first, as well as for second-order Hamiltonian formulations of GR. The distinct role of primary first class constraints, the effect of considering different linear combinations of constraints, the canonical transformations of phase-space variables, and their interplay are discussed in some detail for Hamiltonians of the second- and first-order formulations of metric GR. The first-order formulation of Einstein–Cartan theory, which is the classical background of Loop Quantum Gravity, is also discussed.     

Local Semicircle Law in the Bulk for Gaussian <Emphasis Type="Italic">β</Emphasis>-Ensemble

We use the tridiagonal matrix representation to derive a local semicircle law for Gaussian beta ensembles at the optimal level of n ^?1+δ for any δ>0. Using a resolvent expansion, we first derive a semicircle law at the intermediate level of n ^?1/2+δ ; then an induction argument allows us to reach the optimal level. This result was obtained in a different setting, using different methods, by Bourgade, Erdös, and Yau in arXiv:1104.2272 [math.PR] and Bao and Su in arXiv:1104.3431 [math.PR]. Our approach is new and could be extended to other tridiagonal models.     

Geometric counter-vertex for open string scattering on D-branes

In arXiv:0801.0218 [hep-th] it was conjectured that quantum effects of open strings moving on D-branes generate the D-brane geometry through a counter-vertex operator. The conjecture has been checked at one-loop in arXiv:0806.3330 [hep-th]. Here we discuss the two-loop extension.     

The Vlasov-Poisson-Boltzmann System without Angular Cutoff

This paper is concerned with the Vlasov-Poisson-Boltzmann system for plasma particles of two species in three space dimensions. The Boltzmann collision kernel is assumed to be angular non-cutoff with 3 < γ < ?2s and 1/2 ≤ s < 1, where γ , s are two parameters describing the kinetic and angular singularities, respectively. We establish the global existence and convergence rates of classical solutions to the Cauchy problem when initial data is near Maxwellians. This extends the results in Duan et al. (J Diff Eqs 252(12):6356–6386, 2012, Math Models Methods Appl Sci 23(6):927, 2013) for the cutoff kernel with ?2 ≤ γ ≤ 1 to the case ?3 < γ < ?2 as long as the angular singularity exists instead and is strong enough, i.e., s is close to 1. The proof is based on the time-weighted energy method building also upon the recent studies of the non-cutoff Boltzmann equation in Gressman and Strain (J Amer Math Soc 24(3):771–847, 2011) and the Vlasov-Poisson-Landau system in Guo (J Amer Math Soc 25:759–812, 2012).     

Cross sections for leptophobic topcolor Z′ decaying to top–antitop

We present numerical calculations of the production cross section of a heavy Z?? resonance in hadron?Chadron collisions with subsequent decay into top?Cantitop pairs. In particular, we consider the leptophobic topcolor Z?? discussed under Model IV of hep-ph/9911288, which has predicted cross sections large enough to be experimentally accessible at the Fermilab Tevatron and the Large Hadron Collider at CERN. This article presents an updated calculation valid for the Tevatron and all proposed LHC collision energies. Cross sections are presented for various Z?? widths, in $p\bar{p}$ collisions at $\sqrt{s}=2\mbox{~TeV}$ , and in pp collisions at $\sqrt{s}=7, 8, 10 \mbox{ and } 14\mbox{~TeV}$ .     

Flavour issues for string-motivated heavy scalar spectra with a low gluino mass: the G 2-MSSM case

In recent years it has been learned that scalar superpartner masses and trilinear couplings should both generically be larger than about 20?TeV at the short-distance string scale if our world is described by a compactified string or M-theory with supersymmetry breaking and stabilized moduli (Acharya et?al. in arXiv:1006.3272 [hep-ph], 2010). Here we study implications of this, somewhat generally and also in detail for a particular realization (compactification of M-theory on a G ₂ manifold) where there is significant knowledge of the superpotential and gauge kinetic function, and a light gluino. In a certain sense this yields an ultraviolet completion of minimal flavour violation. Flavour violation stems from off-diagonal and non-universal diagonal elements of scalar mass matrices and trilinear couplings, and from renormalization group running. We also examine stability bounds on the scalar potential. While heavy scalars alone do not guarantee the absence of flavour problems, our studies show that models with heavy scalars and light gluinos can be free from such problems.     

The Absolutely Continuous Spectrum of One-dimensional Schrödinger Operators

This paper deals with general structural properties of one-dimensional Schrödinger operators with some absolutely continuous spectrum. The basic result says that the ω limit points of the potential under the shift map are reflectionless on the support of the absolutely continuous part of the spectral measure. This implies an Oracle Theorem for such potentials and Denisov-Rakhmanov type theorems. In the discrete case, for Jacobi operators, these issues were discussed in my recent paper (Remling, The absolutely continuous spectrum of Jacobi matrices, http://arxiv.org/abs/0706.1101, 2007). The treatment of the continuous case in the present paper depends on the same basic ideas.