Exact Lagrangian submanifolds in simply-connected cotangent bundles

We consider exact Lagrangian submanifolds in cotangent bundles. Under certain additional restrictions (triviality of the fundamental group of the cotangent bundle, and of the Maslov class and second Stiefel-Whitney class of the Lagrangian submanifold) we prove such submanifolds are Floer-cohomologically indistinguishable from the zero-section. This implies strong restrictions on their topology. An essentially equivalent result was recently proved independently by Nadler, using a different approach.Comment: 28 pages, 3 figures. Version 2 -- derivation and discussion of the spectral sequence considerably expanded. Other minor change

The epsilon expansion at next-to-next-to-leading order with small imaginary chemical potential

We discuss chiral perturbation theory for two and three quark flavors in the epsilon expansion at next-to-next-to-leading order (NNLO) including a small imaginary chemical potential. We calculate finite-volume corrections to the low-energy constants $\Sigma$ and $F$ and determine the non-universal modifications of the theory, i.e., modifications that cannot be mapped to random matrix theory (RMT). In the special case of two quark flavors in an asymmetric box we discuss how to minimize the finite-volume corrections and non-universal modifications by an optimal choice of the lattice geometry. Furthermore we provide a detailed calculation of a special version of the massless sunset diagram at finite volume.Comment: 21 pages, 5 figure

Lagrangian Floer superpotentials and crepant resolutions for toric orbifolds

We investigate the relationship between the Lagrangian Floer superpotentials for a toric orbifold and its toric crepant resolutions. More specifically, we study an open string version of the crepant resolution conjecture (CRC) which states that the Lagrangian Floer superpotential of a Gorenstein toric orbifold $\mathcal{X}$ and that of its toric crepant resolution $Y$ coincide after analytic continuation of quantum parameters and a change of variables. Relating this conjecture with the closed CRC, we find that the change of variable formula which appears in closed CRC can be explained by relations between open (orbifold) Gromov-Witten invariants. We also discover a geometric explanation (in terms of virtual counting of stable orbi-discs) for the specialization of quantum parameters to roots of unity which appears in Y. Ruan's original CRC ["The cohomology ring of crepant resolutions of orbifolds", Gromov-Witten theory of spin curves and orbifolds, 117-126, Contemp. Math., 403, Amer. Math. Soc., Providence, RI, 2006]. We prove the open CRC for the weighted projective spaces $\mathcal{X}=\mathbb{P}(1,\ldots,1,n)$ using an equality between open and closed orbifold Gromov-Witten invariants. Along the way, we also prove an open mirror theorem for these toric orbifolds.Comment: 48 pages, 1 figure; v2: references added and updated, final version, to appear in CM

Holomorphic potentials for graded D-branes

We discuss gauge-fixing, propagators and effective potentials for topological A-brane composites in Calabi-Yau compactifications. This allows for the construction of a holomorphic potential describing the low-energy dynamics of such systems, which generalizes the superpotentials known from the ungraded case. Upon using results of homotopy algebra, we show that the string field and low energy descriptions of the moduli space agree, and that the deformations of such backgrounds are described by a certain extended version of `off-shell Massey products' associated with flat graded superbundles. As examples, we consider a class of graded D-brane pairs of unit relative grade. Upon computing the holomorphic potential, we study their moduli space of composites. In particular, we give a general proof that such pairs can form acyclic condensates, and, for a particular case, show that another branch of their moduli space describes condensation of a two-form.Comment: 47 pages, 7 figure

Role of the axial U(1) anomaly in the chiral susceptibility of QCD at high temperature

The chiral susceptibility, or the first derivative of the chiral condensate with respect to the quark mass, is often used as a probe for the QCD phase transition since the chiral condensate is an order parameter of SU(2)L × SU(2)R symmetry breaking. However, the chiral condensate also breaks the axial U(1) symmetry, which is usually not studied as it is already broken by the anomaly and apparently has little impact on the transition. We investigate the susceptibilities in the scalar and pseudoscalar channels in order to quantify how much the axial U(1) breaking contributes to the chiral phase transition. Employing a chirally symmetric lattice Dirac operator and its eigenmode decomposition, we separate the axial U(1) breaking effects from others. Our result in two-flavor QCD indicates that both of the connected and disconnected chiral susceptibilities are dominated by axial U(1) breaking at temperatures T ≳ 190 MeV after the quadratically divergent constant is subtracted

Weak Chaos from Tsallis Entropy

We present a geometric, model-independent, argument that aims to explain why the Tsallis entropy describes systems exhibiting "weak chaos", namely systems whose underlying dynamics has vanishing largest Lyapunov exponent. Our argument relies on properties of a deformation map of the reals induced by the Tsallis entropy, and its conclusion agrees with all currently known results.Comment: 19 pages, Standard LaTeX2e, v2: addition of the last paragraph in Section 4. Three additional refs. To be published in QScience Connec

D-brane categories

This is an exposition of recent progress in the categorical approach to D-brane physics. I discuss the physical underpinnings of the appearance of homotopy categories and triangulated categories of D-branes from a string field theoretic perspective, and with a focus on applications to homological mirror symmetry.Comment: 37 pages, IJMPA styl

Effect of the ionic liquid [bmim]Cl and high pressure on the activity of cellulase

The effect of the ionic liquid 1-butyl-3-methylimidazolium chloride ([bmim]Cl) and of high pressure on the activity of cellulase from Aspergillus niger were studied separately and in combination. The enzyme activity decreased with increasing concentrations of [bmim]Cl, reaching 50% the value in aqueous buffer with 20% [bmim]Cl. However, when the enzyme is held in 10% [bmim]Cl and is then assayed in 1% [bmim]Cl, it showed only 8% reduction of activity. These results can be explained by the fact that the activity of the enzyme in [bmim]Cl is linearly correlated with the decrease of the thermodynamic water activity (aw). Under pressure the enzyme activity varied from less 60% (at 200MPa) to equal (at 400 MPa), compared to atmospheric pressure. In 10% [bmim]Cl under pressure, cellulase activity is improved compared to atmospheric pressure, varying from equal (at 600 MPa) to 1.7-fold higher (at 100 MPa). This opens the possibility to improve cellulase activity in ionic liquids, and possibly of other enzymes, by carrying out the reaction under pressure