Limiting Case of Modified Electroweak Model for Contracted Gauge Group

The modification of the Electroweak Model with 3-dimensional spherical geometry in the matter fields space is suggested. The Lagrangian of this model is given by the sum of the {\it free} (without any potential term) matter fields Lagrangian and the standard gauge fields Lagrangian. The vector boson masses are generated by transformation of this Lagrangian from Cartesian coordinates to a coordinates on the sphere $S_3$. The limiting case of the bosonic part of the modified model, which corresponds to the contracted gauge group $SU(2;j)\times U(1)$ is discussed. Within framework of the limit model Z-boson and electromagnetic fields can be regarded as an external ones with respect to W-bosons fields in the sence that W-boson fields do not effect on these external fields. The masses of all particles of the Electroweak Model remain the same, but field interactions in contracted model are more simple as compared with the standard Electroweak Model.Comment: 12 pages, talk given at the XIII Int. Conf. on SYMMETRY METHODS IN PHYSICS, Dubna, Russia, July 6-9, 2009; added references for introduction, clarified motivatio

Higgsless Electroweak Model and Contraction of Gauge Group

A modified formulation of the Electroweak Model with 3-dimensional spherical geometry in the target space is suggested. The {\it free} Lagrangian in the spherical field space along with the standard gauge field Lagrangian form the full Higgsless Lagrangian of the model, whose second order terms reproduce the same experimentally verified fields with the same masses as the Standard Electroweak Model. The vector bosons masses are automatically generated, so there is no need in special mechanism of spontaneous symmetry breaking. The limiting case of the modified Higgsless Electroweak Model, which corresponds to the contracted gauge group $SU(2;j)\times U(1)$ is discussed. Within framework of the limit model Z-boson, electromagnetic and electron fields are interpreted as an external ones with respect to W-bosons and neutrino fields. The W-bosons and neutrino fields do not effect on these external fields. The masses of all particles remain the same, but the field interactions in contracted model are more simple as compared with the standard Electroweak Model due to nullification of some terms.Comment: Talk at the International Workshop "`Supersymmetries and Quantum Symmetries"' (SQS-09), Dubna, Russia, July 29 -- August 3, 2009, 11

On asymptotic dimension of groups

We prove a version of the countable union theorem for asymptotic dimension and we apply it to groups acting on asymptotically finite dimensional metric spaces. As a consequence we obtain the following finite dimensionality theorems. A) An amalgamated product of asymptotically finite dimensional groups has finite asymptotic dimension: asdim A *_C B < infinity. B) Suppose that G' is an HNN extension of a group G with asdim G < infinity. Then asdim G'< infinity. C) Suppose that \Gamma is Davis' group constructed from a group \pi with asdim\pi < infinity. Then asdim\Gamma < infinity.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-4.abs.htm

Lifting asymptotic degeneracies with the Mirror TBA

We describe a qualitative feature of the AdS_5 x S^5 string spectrum which is not captured by the asymptotic Bethe ansatz. This is reflected by an enhanced discrete symmetry in the asymptotic limit, whereby extra energy degeneracy enters the spectrum. We discuss how finite size corrections should lift this degeneracy, through both perturbative (Luscher) and non-perturbative approaches (the Mirror TBA), and illustrate this explicitly on two such asymptotically degenerate states.Comment: v3, 20 pages, 1 figure, 2 tables, as publishe

Numerical results for the exact spectrum of planar AdS4/CFT3

We compute the anomalous dimension for a short single-trace operator in planar ABJM theory at intermediate coupling. This is done by solving numerically the set of Thermodynamic Bethe Ansatz equations which are expected to describe the exact spectrum of the theory. We implement a truncation method which significantly reduces the number of integral equations to be solved and improves numerical efficiency. Results are obtained for a range of 't Hooft coupling lambda corresponding to $0 \leq h(\lambda) \leq 1$, where h(lambda) is the interpolating function of the AdS4/CFT3 Bethe equations.Comment: v3: corrected Acknowledgements section; v4: minor changes, published version; v5: fixed typos in Eq. (3.9

Wrapping corrections, reciprocity and BFKL beyond the sl(2) subsector in N=4 SYM

We consider N=4 SYM and a class of spin N, length-3, twist operators beyond the well studied sl(2) subsector. They can be identified at one-loop with three gluon operators. At strong coupling, they are associated with spinning strings with two spins in AdS5. We exploit the Y-system to compute the leading weak-coupling four loop wrapping correction to their anomalous dimension. The result is written in closed form as a function of the spin N. We combine the wrapping correction with the known four-loop asymptotic Bethe Ansatz contribution and analyze special limits in the spin N. In particular, at large N, we prove that a generalized Gribov-Lipatov reciprocity holds. At negative unphysical spin, we present a simple BFKL-like equation predicting the rightmost leading poles.Comment: 18 page

TBA, NLO Luscher correction, and double wrapping in twisted AdS/CFT

The ground-state energy of integrably-twisted theories is analyzed in finite volume. We derive the leading and next-to-leading order (NLO) L\"uscher-type corrections for large volumes of the vacuum energy for integrable theories with twisted boundary conditions and twisted S-matrix. We then derive the twisted thermodynamic Bethe ansatz (TBA) equations to describe exactly the ground state, from which we obtain an untwisted Y-system. The two approaches are compared by expanding the TBA equations to NLO, and exact agreement is found. We give explicit results for the O(4) model and for the three-parameter family of $\gamma$-deformed (non-supersymmetric) planar AdS/CFT model, where the ground-state energy can be nontrivial and can acquire finite-size corrections. The NLO corrections, which correspond to double-wrapping diagrams, are explicitly evaluated for the latter model at six loops.Comment: 42 pages, 2 figures, v2: references added, v3: minor correction