170,196 research outputs found
Integrable light-cone lattice discretizations from the universal -matrix
No full textOur goal is to develop a more general scheme for constructing integrable lattice regularisations of integrable quantum field theories. Considering the affine Toda theories as examples, we show how to construct such lattice regularisations using the representation theory of quantum affine algebras. This requires us to clarify in particular the relations between the light-cone approach to integrable lattice models and the representation theory of quantum affine algebras. Both are found to be related in a very natural way, suggesting a general scheme for the construction of generalised Baxter Q-operators. One of the main difficulties we need to deal with is coming from the infinite-dimensionality of the relevant families of representations. It is handled by means of suitable renormalisation prescriptions defining what may be called the modular double of quantum affine algebras. This framework allows us to give a representation-theoretic proof of finite-difference equations generalising the Baxter equation
Bootstrap equations for N = 4 SYM with defects
No full textThis paper focuses on the analysis of 4dN = 4 superconformal theories in the presence of a defect from the point of view of the conformal bootstrap. We will concentrate first on the case of codimension one, where the defect is a boundary that preserves half of the supersymmetry. After studying the constraints imposed by supersymmetry, we will obtain the Ward identities associated to two-point functions of 12 -BPS operators and write their solution as a superconformal block expansion. Due to a surprising connection between spacetime and R-symmetry conformal blocks, our results not only apply to 4dN = 4 superconformal theories with a boundary, but also to three more systems that have the same symmetry algebra: 4dN = 4 superconformal theories with a line defect, 3dN = 4 superconformal theories with no defect, and OSP(4∗|4) superconformal quantum mechanics. The superconformal algebra implies that all these systems possess a closed subsector of operators in which the bootstrap equations become polynomial constraints on the CFT data. We derive these truncated equations and initiate the study of their solutions
Mayer-Cluster Expansion of Instanton Partition Functions and Thermodynamic Bethe Ansatz
No full textIn arXiv:0908.4052, Nekrasov and Shatashvili pointed out that the N=2 instanton partition function in a special limit of the Omega-deformation parameters is characterized by certain thermodynamic Bethe ansatz (TBA) like equations. In this work we present an explicit derivation of this fact as well as generalizations to quiver gauge theories. To do so we combine various techniques like the iterated Mayer expansion, the method of expansion by regions, and the path integral tricks for non-perturbative summation. The TBA equations derived entirely within gauge theory have been proposed to encode the spectrum of a large class of quantum integrable systems. We hope that the derivation presented in this paper elucidates further this completely new point of view on the origin, as well as on the structure, of TBA equations in integrable models
A geometric free field realisation for the genus-two class S theory of type a1
No full textWe present a free field realisation for the vertex operator algebra
associated to the genus-two, class superconformal field theory of
type . The free field realisation is in the style of recent
work by the authors, and is formulated in terms of a one-dimensional isotropic
lattice vertex algebra along with two pairs of symplectic fermions. Our
realisation makes manifest an enhanced outer automorphism group
of the VOA that is inherited from the symplectic fermion system. This extends
an outer automorphism that has been observed in recent work of
Kiyoshige and Nishinaka and significantly simplifies the structure of the
algebra. Along the way, we also produce a realisation of the generic subregular
Drinfel'd-Sokolov algebra of type in terms of the
generic principle algebra of type and a
one-dimensional isotropic lattice vertex algebra
Bootstrapping the half-BPS line defect
No full textWe use modern bootstrap techniques to study half-BPS line defects in 4dN= 4 superconformal theories. Specifically, we consider the 1d CFT with OSP(4∗|4) superconformal symmetry living on such a defect. Our analysis is general and based only on symmetries, it includes however important examples like Wilson and ’t Hooft lines in N= 4 super Yang-Mills. We present several numerical bounds on OPE coefficients and conformal dimensions. Of particular interest is a numerical island obtained from a mixed correlator bootstrap that seems to imply a unique solution to crossing. The island is obtained if some assumptions about the spectrum are made, and is consistent with Wilson lines in planar N= 4 super Yang-Mills at strong coupling. We further analyze the vicinity of the strong-coupling point by calculating perturbative corrections using analytic methods. This perturbative solution has the sparsest spectrum and is expected to saturate the numerical bounds, explaining some of the features of our numerical results
Spectral parameters for scattering amplitudes in N=4 super Yang-Mills theory
No full textPlanar N= 4 Super Yang-Mills theory appears to be a quantum integrable four-dimensional conformal theory. This has been used to find equations believed to describe its exact spectrum of anomalous dimensions. Integrability seemingly also extends to the planar space-time scattering amplitudes of the N= 4 model, which show strong signs of Yangian invariance. However, in contradistinction to the spectral problem, this has not yet led to equations determining the exact amplitudes. We propose that the missing element is the spectral parameter, ubiquitous in integrable models. We show that it may indeed be included into recent on-shell approaches to scattering amplitude integrands, providing a natural deformation of the latter. Under some constraints, Yangian symmetry is preserved. Finally we speculate that the spectral parameter might also be the regulator of choice for controlling the infrared divergences appearing when integrating the integrands in exactly four dimensions. © 2014 The Author(s)
Symmetries of tree-level scattering amplitudes in N=6 superconformal Chern-Simons theory
No full textConstraints of the osp(6|4) symmetry on tree-level scattering amplitudes in N=6 superconformal Chern-Simons theory are derived. Supplemented by Feynman diagram calculations, solutions to these constraints, namely, the four- and six-point superamplitudes, are presented and shown to be invariant under Yangian symmetry. This introduces integrability into the amplitude sector of the theory. © 2010 The American Physical Society
On Correlation Functions of BPS Operators in 3d N= 6 Superconformal Theories
No full textWe introduce a novel harmonic superspace for 3dN=6 superconformal field theories that is tailor made for the study of correlation functions of BPS operators. We calculate a host of two- and three-point functions in full generality and put strong constraints on the form of four-point functions of some selected BPS multiplets. For the four-point function of 12-BPS operators we obtain the associated Ward identities by imposing the absence of harmonic singularities. The latter imply the existence of a solvable subsector in which the correlator becomes topological. This mechanism can be explained by cohomological reduction with respect to a special nilpotent supercharge
Intraoperative neurophysiology of the motor cortex and corticospinal tracts: advantages, limits and future perspectives.
No full textBackground. Brain surgery in motor areas requires a balance between radical surgical resection and risk of postoperative motor deficits. Intraoperative neurophysiological monitoring, especially with motor evoked potentials (MEPs), provides a valuable help in such conditions; however, the correlation between MEP amplitude changes and clinical outcome is not always clear. A stronger neurophysiological predictor of outcome is therefore desirable. Objectives. The aims of this Thesis are: a. to analyze the limits of MEP monitoring during brain surgery in motor areas with a special attention to the confounding factors that may alter the interpretation of MEP changes during surgery; b. to verify and confirm the role of a strong neurophysiological predictor of outcome - the D-wave monitoring - during surgery for intramedullary spinal cord tumor; c. to apply the D-wave monitoring during brain surgery in motor areas. The Thesis is divided in three sections according to the aforementioned objectives. Materials and Methods. In the first section, a consecutive cohort of 157 patients submitted to surgical removal of a tumour adjacent to the motor areas and CST with simultaneous subcortical motor mapping and DCS MEP monitoring were analysed. Motor function was assessed the day after surgery, at discharge, and at further follow-up postoperatively. A post-hoc analysis was conducted in order to analyse possible pre- and postoperative confounding factors during MEP changes interpretation. In the second section, a consecutive cohort of 219 patients submitted to surgery for intramedullary spinal cord tumors (ISCTs) with simultaneous muscle MEP and D-wave monitoring were analysed. Motor function was assessed the day after surgery, at discharge, and at further follow-up postoperatively. A post-hoc analysis was performed in order to verify the reliability of D-wave monitoring as a strong outcome predictor. In the third section, we report the experience of 3 consecutive cases operated on for brain tumors in motor areas with the aid of D-wave monitoring. Results. Section I: the location of the tumour in the prefrontal cortex and along the CST are related with a higher rate of postoperative motor deficits (p=0.04 and p=0.008, respectively); for tumours located in the prefrontal cortex, 53% of patients showed new motor deficit with changes of MEP in 16% of them. Different muscles showed different capability to predict new motor deficits; furthermore, the higher is the number of muscles with MEP amplitude below the threshold, the higher is the probability of a new stable motor deficit. Section II: D-wave monitoring is a valuable help during surgery for ISCTs and show a sensitivity of 33.3%, a specificity of 99.2%; positive predictive value is 50% and negative predictive value is 98.4%. The accuracy calculated is 97.6%. Section III: we were able to record TES D-wave in patients 2 and 3; in patient 1 we obtained the D-wave only with TES of the hemisphere contralateral to the tumour. It was not possible to obtain a clear D-wave from DCS in all three patients. In patients 2 and 3 it was possible to obtain the D-wave through subcortical bipolar stimulation along CST. Conclusions. Intraoperative neurophysiology is a valuable help during surgery in motor areas. MEP monitoring provide useful and reliable information during surgery, but it is not always easy to analyse the relationship between intraoperative changes and clinical outcome. D-wave monitoring is a well-known technique and our results confirmed its role of strong outcome predictor. The application of this technique for brain surgery can help to overcome the limits of MEP monitoring alone
Oscillator Construction of su(n|m) Q-Operators
No full textWe generalize our recent explicit construction of the full hierarchy of Baxter Q-operators of compact spin chains with su(n) symmetry to the supersymmetric case su(n|m). The method is based on novel degenerate solutions of the graded Yang-Baxter equation, leading to an amalgam of bosonic and fermionic oscillator algebras. Our approach is fully algebraic, and leads to the exact solution of the associated compact spin chains while avoiding Bethe ansatz techniques. It furthermore elucidates the algebraic and combinatorial structures underlying the system of nested Bethe equations. Finally, our construction naturally reproduces the representation, due to Z. Tsuboi, of the hierarchy of Baxter Q-operators in terms of hypercubic Hasse diagrams
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