Gravitating global defects: the gravitational field and compactification

We give a prescription to add the gravitational field of a global topological defect to a solution of Einstein's equations in an arbitrary number of dimensions. We only demand that the original solution has a O(n) invariance with n greater or equal 3. We will see that the general effect of a global defect is to introduce a deficit solid angle. We also show how the same kind of scalar field configurations can be used for spontaneous compactification of "n" extra dimensions on an n-sphere.Comment: Uses revte

Higher string functions, higher-level Appell functions, and the logarithmic ^sl(2)_k/u(1) CFT model

We generalize the string functions C_{n,r}(tau) associated with the coset ^sl(2)_k/u(1) to higher string functions A_{n,r}(tau) and B_{n,r}(tau) associated with the coset W(k)/u(1) of the W-algebra of the logarithmically extended ^sl(2)_k conformal field model with positive integer k. The higher string functions occur in decomposing W(k) characters with respect to level-k theta and Appell functions and their derivatives (the characters are neither quasiperiodic nor holomorphic, and therefore cannot decompose with respect to only theta-functions). The decomposition coefficients, to be considered ``logarithmic parafermionic characters,'' are given by A_{n,r}(tau), B_{n,r}(tau), C_{n,r}(tau), and by the triplet \mathscr{W}(p)-algebra characters of the (p=k+2,1) logarithmic model. We study the properties of A_{n,r} and B_{n,r}, which nontrivially generalize those of the classic string functions C_{n,r}, and evaluate the modular group representation generated from A_{n,r}(tau) and B_{n,r}(tau); its structure inherits some features of modular transformations of the higher-level Appell functions and the associated transcendental function Phi.Comment: 34 pages, amsart++, times. V2: references added; minor changes; some nonsense in B.3.3. correcte

Multisymplectic approach to integrable defects in the sine-Gordon model

Ideas from the theory of multisymplectic systems, introduced recently in integrable systems by the author and Kundu to discuss Liouville integrability in classical field theories with a defect, are applied to the sine-Gordon model. The key ingredient is the introduction of a second Poisson bracket in the theory that allows for a Hamiltonian description of the model that is completely equivalent to the standard one, in the absence of a defect. In the presence of a defect described by frozen Bäcklund transformations, our approach based on the new bracket unifies the various tools used so far to attack the problem. It also gets rid of the known issues related to the evaluation of the Poisson brackets of the defect matrix which involve fields at coinciding space point (the location of the defect). The original Lagrangian approach also finds a nice reinterpretation in terms of the canonical transformation representing the defect conditions

Boundary Reflection Matrix for D4(1)D_4^{(1)} Affine Toda Field Theory

We present one loop boundary reflection matrix for $d_4^{(1)}$ Toda field theory defined on a half line with the Neumann boundary condition. This result demonstrates a nontrivial cancellation of non-meromorphic terms which are present when the model has a particle spectrum with more than one mass. Using this result, we determine uniquely the exact boundary reflection matrix which turns out to be \lq non-minimal' if we assume the strong-weak coupling \lq duality'.Comment: 14 pages, Late

A & B model approaches to surface operators and Toda theories

It has recently been argued by Alday et al that the inclusion of surface operators in 4d N=2 SU(2) quiver gauge theories should correspond to insertions of certain degenerate operators in the dual Liouville theory. So far only the insertion of a single surface operator has been treated (in a semi-classical limit). In this paper we study and generalise this proposal. Our approach relies on the use of topological string theory techniques. On the B-model side we show that the effects of multiple surface operator insertions in 4d N=2 gauge theories can be calculated using the B-model topological recursion method, valid beyond the semi-classical limit. On the mirror A-model side we find by explicit computations that the 5d lift of the SU(N) gauge theory partition function in the presence of (one or many) surface operators is equal to an A-model topological string partition function with the insertion of (one or many) toric branes. This is in agreement with an earlier proposal by Gukov. Our A-model results were motivated by and agree with what one obtains by combining the AGT conjecture with the dual interpretation in terms of degenerate operators. The topological string theory approach also opens up new possibilities in the study of 2d Toda field theories.Comment: 43 pages. v2: Added references, including a reference to unpublished work by S.Gukov; minor changes and clarifications

Type-II B\"acklund Transformations via Gauge Transformations

The construction of type II Backlund transformation for the sine-Gordon and the Tzitzeica-Bullough-Dodd models are obtained from gauge transformation. An infinite number of conserved quantities are constructed from the defect matrices. This guarantees that the introduction of type II defects for these models does not spoil their integrability. In particular, modified energy and momentum are derived and compared with those presented in recent literature.Comment: Latex 19 pages, 2 tables. v2: Comments and two references adde

Giant magnons and non-maximal giant gravitons

We produce the open strings on $\mathbb{R}\times S^{2}$ that correspond to the solutions of integrable boundary sine-Gordon theory by making use of the $N$-magnon solutions provided in \cite{KPV} together with explicit moduli. Relating the two boundary parameters in a special way we describe the scattering of giant magnons with non-maximal $Y=0$ giant gravitons and calculate the leading contribution to the associated magnon scattering phase.Comment: 34 pages, 8 figure

Nucleation of (4)R^{(4)}R Brane Universes

The creation of brane universes induced by a totally antisymmetric tensor living in a fixed background spacetime is presented, where a term involving the intrinsic curvature of the brane is considered. A canonical quantum mechanical approach employing Wheeler-DeWitt equation is done. The probability nucleation for the brane is calculated taking into account both an instanton method and a WKB approximation. Some cosmological implications arose from the model are presented.Comment: 19 pages, 2 figure

Radiation damage in the LHCb vertex locator

The LHCb Vertex Locator (VELO) is a silicon strip detector designed to reconstruct charged particle trajectories and vertices produced at the LHCb interaction region. During the first two years of data collection, the 84 VELO sensors have been exposed to a range of fluences up to a maximum value of approximately 45 × 1012 1 MeV neutron equivalent (1 MeV neq). At the operational sensor temperature of approximately −7 °C, the average rate of sensor current increase is 18 μA per fb−1, in excellent agreement with predictions. The silicon effective bandgap has been determined using current versus temperature scan data after irradiation, with an average value of Eg = 1.16±0.03±0.04 eV obtained. The first observation of n+-on-n sensor type inversion at the LHC has been made, occurring at a fluence of around 15 × 1012 of 1 MeV neq. The only n+-on-p sensors in use at the LHC have also been studied. With an initial fluence of approximately 3 × 1012 1 MeV neq, a decrease in the Effective Depletion Voltage (EDV) of around 25 V is observed. Following this initial decrease, the EDV increases at a comparable rate to the type inverted n+-on-n type sensors, with rates of (1.43±0.16) × 10−12 V/ 1 MeV neq and (1.35±0.25) × 10−12 V/ 1 MeV neq measured for n+-on-p and n+-on-n type sensors, respectively. A reduction in the charge collection efficiency due to an unexpected effect involving the second metal layer readout lines is observed

A multisymplectic approach to defects in integrable classical field theory

We introduce the concept of multisymplectic formalism, familiar in covariant field theory, for the study of integrable defects in 1+1 classical field theory. The main idea is the coexistence of two Poisson brackets, one for each spacetime coordinate. The Poisson bracket corresponding to the time coordinate is the usual one describing the time evolution of the system. Taking the nonlinear Schr\"odinger (NLS) equation as an example, we introduce the new bracket associated to the space coordinate. We show that, in the absence of any defect, the two brackets yield completely equivalent Hamiltonian descriptions of the model. However, in the presence of a defect described by a frozen B\"acklund transformation, the advantage of using the new bracket becomes evident. It allows us to reinterpret the defect conditions as canonical transformations. As a consequence, we are also able to implement the method of the classical r matrix and to prove Liouville integrability of the system with such a defect. The use of the new Poisson bracket completely bypasses all the known problems associated with the presence of a defect in the discussion of Liouville integrability. A by-product of the approach is the reinterpretation of the defect Lagrangian used in the Lagrangian description of integrable defects as the generating function of the canonical transformation representing the defect conditions