On Type II strings in exact superconformal non-constant RR backgrounds

An explicitly exact superconformal description is provided to some classes of Type II string theories in non constant RR backgrounds. This is done by applying the manifest (2,2) approach of Berkovits and Maldacena to Type II strings and by studying the condition of exact conformal invariance of certain supersymmetric backgrounds. We find a new set of exact type IIA strings with non constant RR 2-form and 4-form curvatures and for type IIB with non constant 3-form curvature.Comment: 15 pages; typos and a reference adde

Interacting Strings in Matrix String Theory

It is here explained how the Green-Schwarz superstring theory arises from Matrix String Theory. This is obtained as the strong YM-coupling limit of the theory expanded around its BPS instantonic configurations, via the identification of the interacting string diagram with the spectral curve of the relevant configuration. Both the GS action and the perturbative weight $g_s^{-\chi}$, where $\chi$ is the Euler characteristic of the world-sheet surface and $g_s$ the string coupling, are obtained.Comment: 11 pages, no figures, two references adde

N=2 SYM RG Scale as Modulus for WDVV Equations

We derive a new set of WDVV equations for N=2 SYM in which the renormalization scale $\Lambda$ is identified with the distinguished modulus which naturally arises in topological field theories.Comment: 6 pages, LaTe

Matone's relation of N=2 super Yang-Mills and spectrum of Toda chain

In N=2 super Yang-Mills theory, the Matone's relation relates instanton corrections of the prepotential to instanton corrections of scalar field condensation . This relation has been proved to hold for Omega deformed theories too, using localization method. In this paper, we first give a case study supporting the relation, which does not rely on the localization technique. Especially, we show that the magnetic expansion also satisfies a relation of Matone's type. Then we discuss implication of the relation for the spectrum of periodic Toda chain, in the context of recently proposed Nekrasov-Shatashvili scheme.Comment: 17 pages; v2 minor changes, references added; v3 more material added in 2nd section, clarification in 4th sectio

N=2 Sigma Models for Ramond-Ramond Backgrounds

Using the U(4) hybrid formalism, manifestly N=(2,2) worldsheet supersymmetric sigma models are constructed for the Type IIB superstring in Ramond-Ramond backgrounds. The Kahler potential in these N=2 sigma models depends on four chiral and antichiral bosonic superfields and two chiral and antichiral fermionic superfields. When the Kahler potential is quadratic, the model is a free conformal field theory which describes a flat ten-dimensional target space with Ramond-Ramond flux and non-constant dilaton. For more general Kahler potentials, the model describes curved target spaces with Ramond-Ramond flux that are not plane-wave backgrounds. Ricci-flatness of the Kahler metric implies the on-shell conditions for the background up to the usual four-loop conformal anomaly.Comment: 19 pages harvma

A Representation of Symmetry Generators for the Type IIB Superstring on a Plane Wave in the U(4) Formalism

We calculate the symmetry currents for the type IIB superstring on a maximally supersymmetric plane wave background using the N=(2,2) superconformally covariant U(4) formulation developed by Berkovits, Maldacena and Maoz. An explicit realization of the U(4) generators together with 16 fermionic generators is obtained in terms of the N=(2,2) worldsheet fields. Because the action is no longer quadratic, we use a light-cone version to display the currents in terms of the covariant worldsheet variables.Comment: 9 pages, harvmac, Corrected some typographical errors, Added reference

Nonperturbative Relations in N=2 SUSY Yang-Mills and WDVV equation

We find the nonperturbative relation between $\langle {\rm tr} \phi^2 \rangle$, $\langle {\rm tr} \phi^3\rangle$ the prepotential ${\cal F}$ and the vevs $\langle \phi_i\rangle$ in $N=2$ supersymmetric Yang-Mills theories with gauge group $SU(3)$. Nonlinear differential equations for ${\cal F}$ including the Witten -- Dijkgraaf -- Verlinde -- Verlinde equation are obtained. This indicates that $N=2$ SYM theories are essentially topological field theories and that should be seen as low-energy limit of some topological string theory. Furthermore, we construct relevant modular invariant quantities, derive canonical relations between the periods and investigate the structure of the beta function by giving its explicit form in the moduli coordinates. In doing this we discuss the uniformization problem for the quantum moduli space. The method we propose can be generalized to $N=2$ supersymmetric Yang-Mills theories with higher rank gauge groups.Comment: 12 pages, LaTex. Expanded version. New results, corrections, references and acknowledgements adde

Topological String on OSP(1|2)/U(1)

We propose an equivalence between topological string on OSP(1|2)/U(1) and \hat{c} \leq 1 superstring with N=1 world-sheet supersymmetry. We examine this by employing a free field representation of OSP(1|2) WZNW model and find an agreement on the spectrum. We also analyze this proposal at the level of scattering amplitudes by applying a map between correlation functions of OSP(1|2) WZNW model and those of N=1 Liouville theory.Comment: 25 pages, refereces adde

Taming open/closed string duality with a Losev trick

A target space string field theory formulation for open and closed B-model is provided by giving a Batalin-Vilkovisky quantization of the holomorphic Chern-Simons theory with off-shell gravity background. The target space expression for the coefficients of the holomorphic anomaly equation for open strings are obtained. Furthermore, open/closed string duality is proved from a judicious integration over the open string fields. In particular, by restriction to the case of independence on continuous open moduli, the shift formulas of [7] are reproduced and shown therefore to encode the data of a closed string dual.Comment: 22 pages, no figures; v.2 Refs. and a comment added

Brookite, a sometimes under evaluated TiO2polymorph

Some of the advancements concerning the study of phase-pure brookite and, especially, brookite-containing TiO2 mixed phases are reviewed. Relevance is given to their prospective photocatalytic applications, where the (positive) effect of the presence of brookite has been demonstrated, especially when solar light is concerned. From the literature, it emerges that, besides the band gap determination, which still requires more detailed studies (band gap values in a wide range are reported), the roles of brookite-containing heterojunctions, of the surface properties (i.e. acidity, redox behaviour, and the presence of coordinatively unsaturated sites), of the particular crystalline structure and of brookite influence on the anatase to rutile transition are crucial for its applications in the field of (solar) photocatalysis and electrocatalysis, but also electrochemical applications (i.e. Li batteries). The need emerges for a deeper understanding of the physico-chemical phenomena underlying their (recently demonstrated) capacity of stabilizing photogenerated electron/hole pairs. In perspective, the development of green synthesis methods to tailor the surface and structural properties of phase-pure brookite and brookite-containing mixed phases could extend their photo- and electrochemical applications