SUSY field theories, integrable systems and their stringy/brane origin -- II

Five and six dimensional SUSY gauge theories, with one or two compactified directions, are discussed. The 5d theories with the matter hypermultiplets in the fundamental representation are associated with the twisted $XXZ$ spin chain, while the group product case with the bi-fundamental matter corresponds to the higher rank spin chains. The Riemann surfaces for $6d$ theories with fundamental matter and two compact directions are proposed to correspond to the $XYZ$ spin chain based on the Sklyanin algebra. We also discuss the obtained results within the brane and geometrical engeneering frameworks and explain the relation to the toric diagrams.Comment: LaTeX, 21 pages, no figure

Anomalous Chiral Fermi Surface

We provide a geometrical argument for the emergence of a Wess-Zumino-Witten (WZW) term for a Fermi surface threaded by a Berry curvature. In the presence of external fields, the gauged WZW term yields a chiral (triangle) anomaly for the fermionic current at the edge of the Fermi surface. Fermion number is conserved though since the Berry curvatures occur always in pairs with opposite (monopole) charge. The anomalous vector and axial currents for a a fermionic fluid at low temperature threaded by pairs of Berry curvatures are discussed. The leading temperature correction to the chiral vortical effect in a slowly rotating Fermi surface threaded by a Berry curvature maybe tied to the gravitational anomaly.Comment: 4 pages; version to appear in PR

The Classical rr-Matrix for the Relativistic Ruijsenaars-Schneider System

We compute the classical $r$-matrix for the relativistic generalization of the Calogero-Moser model, or Ruijsenaars-Schneider model, at all values of the speed-of-light parameter $\lambda$. We connect it with the non-relativistic Calogero-Moser $r$-matrix $(\lambda \rightarrow -1)$ and the $\lambda = 1$ sine-Gordon soliton limit.Comment: LaTeX file, no figures, 8 page

Big Bang in AdS5AdS_{5} with external field and flat 4d Universe

We describe spontaneous creation of the Brane World in $AdS_{5}$ with external field. The resulting Brane World consists of a flat 4d spatially finite expanding Universe and curved expanding "regulator" branes. No negative tension branes are involved.Comment: Latex, 11 pages, 5 eps figures, references adde

Dualities in integrable systems and N=2 theories

We discuss dualities of the integrable dynamics behind the exact solution to the N=2 SUSY YM theory. It is shown that T duality in the string theory is related to the separation of variables procedure in dynamical system. We argue that there are analogues of S duality as well as 3d mirror symmetry in the many-body systems of Hitchin type governing low-energy effective actions.Comment: 16 pages, Latex, Talk given at QFTHEP-99, Moscow, May 27-June

On spin chains and field theories

We point out that the existence of global symmetries in a field theory is not an essential ingredient in its relation with an integrable model. We describe an obvious construction which, given an integrable spin chain, yields a field theory whose 1-loop scale transformations are generated by the spin chain Hamiltonian. We also identify a necessary condition for a given field theory to be related to an integrable spin chain. As an example, we describe an anisotropic and parity-breaking generalization of the XXZ Heisenberg spin chain and its associated field theory. The system has no nonabelian global symmetries and generally does not admit a supersymmetric extension without the introduction of more propagating bosonic fields. For the case of a 2-state chain we find the spectrum and the eigenstates. For certain values of its coupling constants the field theory associated to this general type of chain is the bosonic sector of the Leigh-Strassler deformation of N=4 SYM theory.Comment: 22 pages, Latex; v2. typos correcte

The structure functions of longitudinal virtual photon at low virtualities

The structure functions of longitudinal virtual photon at low virtualities are calculated in the framework of chiral pertubation theory(ChPT) in the zero and first order of ChPT. It is assumed that the virtuality of target longitudinal photon is much less than the virtuality of the hard projectile photon and both are less than the characteristic ChPT scale.Comment: 16 pages, 8 figure

Spectral Duality in Integrable Systems from AGT Conjecture

We describe relationships between integrable systems with N degrees of freedom arising from the AGT conjecture. Namely, we prove the equivalence (spectral duality) between the N-cite Heisenberg spin chain and a reduced gl(N) Gaudin model both at classical and quantum level. The former one appears on the gauge theory side of the AGT relation in the Nekrasov-Shatashvili (and further the Seiberg-Witten) limit while the latter one is natural on the CFT side. At the classical level, the duality transformation relates the Seiberg-Witten differentials and spectral curves via a bispectral involution. The quantum duality extends this to the equivalence of the corresponding Baxter-Schrodinger equations (quantum spectral curves). This equivalence generalizes both the spectral self-duality between the 2x2 and NxN representations of the Toda chain and the famous AHH duality