Unless otherwise stated, seminars will take place in Cramond Room of the ICMS at the University of Edinburgh.
Friday, 18 July 2014 at 16:00
Eric Sharpe (Virginia Tech)
In this talk I will survey recent progress in heterotic string compactifications and two-dimensional theories with (0,2) supersymmetry. For the first half of the talk, I will give an overview of quantum sheaf cohomology,' a heterotic analogue or generalization of quantum cohomology. For the second half of the talk, I will discuss various new and old dualities in two dimensions. Specifically, I will first review progress towards (0,2) mirror symmetry, a generalization of ordinary mirror symmetry. I'll then turn to gauge dualities in two dimensions, and how easy bits of math can be used to derive such dualities. Finally, I'll discuss decomposition for two-dimensional nonabelian gauge theories with center-invariant matter, which is the observation that such theories can decompose into a disjoint union of closely related theories.
Tuesday, 1 July 2014 at 15:00
Marco Benini (Pavia U)
The generally covariant approach to quantum field theory is reviewed for the simple example of the Klein-Gordon field under a slightly different perspective. The basic idea is to assign to each globally hyperbolic spacetime a suitable space of linear functionals to test solutions of the field equation. The choice of functionals is made in such a way that the evaluation on solutions defines a non-degenerate pairing. It turns out that this perspective reproduces the result of the usual approach. In a second moment, a quantization prescription is applied. In the second part of the talk, we focus the attention on linear gauge theories in the context of general local covariance. We illustrate how, for a simple model, namely Maxwell $k$-forms, the perspective presented in the first part (adapted to gauge theories) provides a definite answear for the choice of functionals to be used to test field configurations. An explicit characterization of this space of functionals can be obtained by means of standard Poincare' duality for de Rham cohomology and its analogue for causally restricted supports.
Wednesday, 11 June 2014 at 14:30
Magnus Goffeng (Hannover U)
This is intended as a quick introduction to noncommutative geometry from the perspective of analysis. Starting from the Weyl law, we will discuss applications and drawback of these techniques by means of examples.
Wednesday, 4 June 2014 at 16:00
Paul Feehan (Rutgers)
Given a compact Lie group and a principal bundle over a closed Riemannian manifold, the quotient space of connections, modulo the action of the group of gauge transformations, has fundamental significance for algebraic geometry, low-dimensional topology, the classification of smooth four-dimensional manifolds, and high-energy physics. The quotient space of connections is equipped with the Yang-Mills energy functional and Atiyah and Bott (1983) had proposed that its gradient flow with respect to the natural Riemannian metric on the quotient space should prove to be an important tool for understanding the topology of the quotient space via an infinite-dimensional Morse theory. The critical points of the energy functional are gauge-equivalence classes of Yang-Mills connections. However, thus far, smooth solutions to the Yang-Mills gradient flow have only been known to exist for all time and converge to critical points, as time tends to infinity, in relatively few cases, including (1) when the base manifold has dimension two or three (Rade, 1991 and 1992, in dimension two and three; G. Daskalopoulos, 1989 and 1992, in dimension two), (2) when the base manifold is a complex algebraic surface (Donaldson, 1985), and (3) in the presence of rotational symmetry in dimension four (Schlatter, Struwe, and Tahvildar-Zadeh, 1998). Global existence of solutions with up to finitely many point singularities (caused by the `bubbling'' phenomenon) at up to finitely many times was proved independently by Struwe (1994) and Kozono, Maeda, and Naito (1995). However, the question of global existence and convergence of smooth solutions over general compact, Riemannian, four-dimensional base manifolds has thus far remained unresolved. In this talk we shall describe our proof of the following result: Given a compact Lie group and a smooth initial connection on a principal bundle over a compact, Riemannian, four-dimensional manifold, there is a unique, smooth solution to the Yang-Mills gradient flow which exists for all time and converges to a smooth Yang-Mills connection on the given principal bundle as time tends to infinity.
Wednesday, 21 May 2014
14:30
Pieter Blue (UoE)
This talk will present decay results for the wave equation and the Maxwell field outside a slowly rotating Kerr black hole. The main results will be the existence of uniformly bounded energies and Morawetz, or integrated local energy decay, estimates. The talk will also explain the relevance of these results to the black hole stability problem. The role of the Killing tensor will also be discussed.
16:00
David Berman (Queen Mary U)
Double field theory and extended geometric theories will be reviewed along with recent results on interpreting wave solutions in extended geometries.
Wednesday, 14 May 2014 at 15:00
Sergey Cherkis (U Arizona)
Monopole dynamics provides plentiful information about both gravitational instantons and about quantum field theories in various dimensions. Doubly periodic monopoles, which are the subject of this talk, are of particular interest, as their moduli spaces are expected to be the spaces of vacua of five-dimensional quantum theories compactified on a two-torus. At the same time, when four-dimensional, these moduli spaces are self-dual gravitational instantons of lowest volume growth. In this talk we identify all doubly periodic monopoles with four moduli. For a general case we commute the asymptotic metric on the moduli space. Surprisingly, the answer is best given in terms of crystals, secondary polytopes, and amoebas.
Wednesday, 7 May 2014
14:30
Gerard Watts (King's College)
W-algebras have been around since 1986, and recently have been discussed in the context of black holes in higher-spin theories in AdS3. I discuss W-algebras, physical models in which they arise and their representations and in particular the modular properties of characters of the W3 algebra.
16:00
Gary Gibbons (DAMTP, Cambridge)
This will be a survey for a general audience of the soliton concept (in Coleman's the sense of Classical Lumps) and will also cover the extent to which black holes may be regarded as solitons.
This talk will take place within the North British Mathematical Physics Seminar series
Wednesday, 26 March 2014 at 13:45
UoE King's buildings, Daniel Rutherford building, Lecture Theatre 2
Dan Waldram (Imperial College)
The study of consistent truncations of gravitational theories is an old subject going back to work of Jordan and Pauli. It is well known that reductions on group manifolds are consistent, but there is also a mysterious set of truncations on very particular coset manifolds with non-trivial form- field fluxes. We show how generalised geometry gives a unified description of such reductions. In particular we demonstrate that all round-sphere S^d geometries admit "generalised parallelisations", giving a simple way to understand the remarkable consistent truncations on S7, S5 and S4.
Wednesday, 5 March 2014
14:30
Alessandro Torrielli (U Surrey)
We review recent progress in understanding the exact scattering theory for strings propagating in AdS_3 backgrounds. We will highlight the role of Yangians, with particular emphasis put on the new features displayed by this case when compared to the AdS_5 background, and discuss the issues of massless modes in the theory.
16:00
Stefano Bolognesi (Durham U)
The Sakai-Sugimoto model is the preeminent example of a string theory description of holographic QCD, in which baryons correspond to topological solitons in the bulk. Here we investigate the validity of various approximations of the Sakai-Sugimoto soliton that are used widely to study the properties of holographic baryons. These different approaches have produced contradictory results in the literature regarding properties of the baryon, such as relations for the electromagnetic form factors. Our analysis clarifies the source of the contradictory results in the literature and resolves some outstanding issues. We provide the first numerical computation of the Sakai-Sugimoto soliton and demonstrate that the numerical results support our analysis. Multi-solitons and solitons with finite density are currently beyond numerical field theory computations. Various approximations have been applied to investigate these important issues and have led to proposals for finite density configurations that include dyonic salt and baryonic popcorn. We introduce and investigate a low-dimensional analogue of the Sakai-Sugimoto model, in which the bulk soliton can be approximated by a flat space sigma model instanton. The advantage of the lower-dimensional theory is that numerical simulations of multi-solitons and finite density solutions can be performed and compared with flat space instanton approximations. In particular, analogues of dyonic salt and baryonic popcorn configurations are found and analysed.
Wednesday, 19 February 2014
13:00
Luca Griguolo and Domenico Seminara (U Parma and U Florence)
Preseminar for PhD students
14:30
Luca Griguolo (U Parma)
We introduce a class of supersymmetric Wilson loops in ABJ(M) theories, with contours lying on a two-sphere. Fermionic and bosonic degrees of freedom couple directly to the loop through a suitable super-connection. These WL generalize the familiar 1/2 BPS case, of which we briefly discuss the exact expression obtained through localization and its matrix model representation. We present the complete two-loop analysis of "latitude" loops and discuss their cohomological relation with a class of purely bosonic loop. Using the latitude, we propose an all-loop formula for the Bremsstrahlung function in ABJM theory, is shown to be consistent with the cusp computation, both at weak and a strong coupling.
16:00
Domenico Seminara (U Florence)
After recalling the basic features of globally and locally supersymmetric Wilson loops in ABJM theories, we shall discuss how to define a loop observable which captures a simple generalization of the quark-antiquark potential. The advantage of this observables is that can be connected to exactly computable BPS quantity in different limits. Finally, we discuss its perturbative analysis both at weak and at strong coupling remarking some important difference with what occurs in N=4 SYM.
Wednesday, 5 February 2014
13:00
Christian Voigt (U Glasgow)
Preseminar for PhD students
14:30
Christian Voigt (U Glasgow)
Clifford algebras and spin groups play a basic role in quantum mechanics and the analysis of Dirac operators. The string group shows up in a similar way in the study of supersymmetric sigma models. In this talk I will explain a suitable analogue of complex Clifford algebras in this setting. The construction is based on fermionic vertex superalgebras and their representation categories, and can be viewed as an instance of categorification.
16:00
Patrick Öhberg (HW)
In this talk we will discuss how artificial gauge fields can be induced in ultracold and charge neutral atomic gases. After a general introduction we will consider in particular density dependent gauge potentials, and how an interacting gauge theory appears in these systems. We show how in such a situation novel topological states in the ultracold gas can exist. We find in particular that the onset of persistent currents in a ring geometry is governed by a critical number of particles. The density-dependent gauge potential is also found to support chiral solitons in a quasi-one-dimensional ultracold Bose gas.
Wednesday, 22 January 2014
13:00
Alessandro Valentino (U Hamburg)
Preseminar for PhD students
14:30
Alessandro Valentino (U Hamburg)
I will talk about a recent geometric approach to realize Dijkgraaf-Witten theories as extended three-dimensional topological quantum field theories over manifolds with boundaries and surface defects.
16:00
Gabor Etesi (Budapest University of Technology and Economics)
In this talk we review some recent results on the analytical aspects of Yang--Mills instanton theory over asymptotically locally flat (ALF) spaces. Firstly we identify natural boundary conditions to be imposed at infinity on self-dual connections in order to make the corresponding moduli spaces well-behaving. Secondly we calculate the virtual dimensions of the instanton moduli spaces by the aid of the Hausel--Hunsicker--Mazzeo (HHM) compactification of an ALF space. In the case of the 1-Taub--NUT space the moduli space of framed SU(2) instantons with unit energy will be constructed explicitly. Thirdly we call attention to a nice geometrical 4d YM/2d CFT duality in the ALF scenario. More precisely the HHM compactification is obtained by attaching a compact surface to the ALF space representing the infinity of the original ALF space. We argue that some data of a 4d quantum SU(2) gauge theory on an ALF space can be encoded into a 2d quantum conformal field theory on this attached surface. All of these are joint works with T. Hausel, M. Jardim and Sz. Szabo.
Friday, 17 January 2014 at 13:00
Azat Gaynutdinov (Institut de Physique Theorique, CEA-Saclay)
Deformed Virasoro algebra introduced in the middle of 90's resembles the well-known deformation of Jack to Macdonald polynomials. More precisely, singular vectors in Verma modules over the Virasoro algebra are Jack polynomials while singular vectors for the deformed Virasoro are described by Macdonald polynomials. Such a natural deformation of the Virasoro algebra appeared to be useful in many applications to off-critical statistical models and massive integrable field theories. In the talk, I present my recent results on a surprising realization of this algebra in finite and critical quantum spin-chains when the deformation parameters are at roots of unity. More formally, it turns out that the deformed Virasoro at N-th root of unity has representations realized by the Temperley-Lieb algebras with N generators. Such finite-dimensional representations are of the cyclic type (similar to those for quantum groups at roots of unity) and were never observed before.
Wednesday, 11 December 2013
14:30
Kirill Krasnov (Nottingham)
I will describe a large class of gauge theories in four dimensions. In the most compact formulation, these theories are described by an action principle that is a functional of only the gauge field. In particular, no metric appears in the Lagrangian or is used in the construction of the theory. The Euler-Lagrange equations are second order PDE's on the gauge field. When the gauge group is taken to be SO(3), a particular theory from this class can be seen to be (classically) equivalent to Einstein's General Relativity. All other points in the SO(3) theory space are still theories of interacting gravitons, and I will sketch how their nature can be clarified by computing the associated graviton scattering amplitudes. I will also explain why this class of gravity theories may be important for quantum gravity. Finally, I will explain how for larger gauge groups containing SO(3) as a subgroup diffeomorphism invariant gauge theories can be seen to describe gravity plus Yang-Mills gauge fields.
16:00
Christian Sämann (HW)
I will discuss a categorified version of the IKKT matrix model based on semistrict Lie 2-algebras. After defining this model, I will demonstrate how standard results of the IKKT model appear in the categorified setting. In particular, I will show that quantized 2-plectic manifolds give vaccuum solutions of the model.
Wednesday, 4 December 2013
13:00
Nicolas Behr (HW)
Preseminar for PhD students
14:30
John Barrett (Nottingham)
The talk will give a general construction for real spectral triples having the algebra of coordinates the n x n matrices. The fuzzy sphere and other examples will be discussed in this framework. There will be a brief discussion of the relevance of this geometry to matrix models and state sum models.
16:00
Nicolas Behr (HW)
Reporting on recent results with A. Konechny (1310.4185), I will talk about the important role redundant operators play in the renormalization of 2d QFTs in the vicinity of conformal fixed points. The origin of the phenomenon of redundancy lies in the necessary modification of the local Weyl anomaly equation to include terms with vector currents for theories with redundant operators. The consequences of these terms are analyzed by means of a technique akin to H. Osborn's local RG technique. Essential details are the formulation of an additional anomaly equation aka redundancy anomaly equation, Wess-Zumino consistency conditions the two anomaly equations must fulfill, and accordingly a large number of relations between the various terms of the anomaly equations. These relations encode the geometry of coupling space and of RG flows, amongst other consequences allowing to interpret the redundancy as a symmetry acting on coupling space. Physical quantities such as the beta-functions or the c-function are invariant under this symmetry, and various other statements may be derived from either the general analysis or in conformal perturbation theory. As an illustration, a few explicit examples (current-current perturbed WZW models) will be presented. I will provide a preseminar with an introduction to Osborn's local RG technique and on the derivtion of the c-theorem in 2d as an illustrating example.
Wednesday, 13 November 2013
13:00
Stefano Kovacs (Dublin Institute for Advanced Studies)
Preseminar for PhD students
14:30
Stefano Kovacs (Dublin Institute for Advanced Studies)
I will present a proposal for studying the AdS_4/CFT_3 correspondence formulated by Aharony, Bergman, Jafferis and Maldacena (ABJM) in a genuinely M-theoretic regime. By focussing on a large angular momentum sector, it is possible to study the duality in a regime in which the gravitational background is eleven-dimensional and the physical states correspond to M2-brane excitations. On the gravity side this sector is well approximated by the pp-wave matrix model, which is weakly coupled. The dual gauge theory description involves monopole operators and a perturbative expansion can be constructed in the form of a Born-Oppenheimer approximation. I will show how the spectra computed on the two sides agree at leading order, thus extending the validity of the ABJM duality beyond the previously considered type IIA limit. The agreement also provides an independent test of the matrix model approach to M-theory.
16:00
Joan Simon (UE)
We will review the importance of Hawking's calculation and some of the paradoxes it leads. We will then get inspired by the problem of thermalization in quantum mechanics to use quantum information tools to compute the size of the corrections to thermal behaviour in quantum mechanics. We will conclude with some lessons that we may extract from these for the physics of black holes.
Wednesday, 23 October 2013
13:00
Daniel Plencner (LMU Munich)
Preseminar for PhD students
14:30
Daniel Plencner (LMU Munich)
Orbifolding a 2-dimensional quantum field theory by a symmetry group admits an elegant description in terms of defect lines and their junction fields. This perspective offers a natural generalization of the concept of an orbifold, in which the role of the symmetry group is replaced by a defect with the structure of a (symmetric) separable Frobenius algebra. In this talk I will focus on the case of Landau-Ginzburg models, in which defects are described by matrix factorizations. After introducing the generalized twisted sectors and discussing topological bulk and boundary correlators in these sectors, I will present a simple proof of the Cardy condition and discuss some further consistency checks on the generalized orbifold theory. This talk is based on arXiv:1307.3141 with Ilka Brunner and Nils Carqueville.
16:00
Branislav Jurco (Charles University, Prague)
We discuss noncommutative gauge theory from the generalized geometry point of view. We argue that the equivalence between the commutative and semiclassically noncommutative DBI actions is naturally encoded in the generalized geometry of D-branes. We comment on a possible generalization to M5-brane.
Wednesday, 9 October 2013
13:00
Guido Franchetti (HW)
Preseminar for PhD students
14:30
Guido Franchetti (HW)
This talk will review recent work done by Nick Manton and myself in the geometric models of matter framework, whose goal is to describe elementary particles in terms of Riemannian 4-manifolds. In particular I will discuss the use of ALF A_k and D_k gravitational instantons to model systems of charged particles and the construction of energy functionals which reproduce the Coulomb interaction energy of such particle systems out of the topological and geometrical properties of ALF gravitational instantons.
16:00
Anastasia Doikou (HW)
A systematic approach to classical integrable defects is proposed, based on an underlying Poisson algebraic structure. Local integrals of motions are constructed as well as the time components of the corresponding Lax pairs for the sine-Gordon model. Continuity conditions imposed upon the time components of the Lax pair to all orders give rise to sewing conditions, which turn out to be compatible with the hierarchy of charges in involution. At the quantum level, using the Bethe ansatz methodology, we extract the transmission amplitudes for the XXZ model. These describe the interaction between the particle-like excitations displayed by the model and the spin impurity. In the attractive regime of the XXZ model, we also derive the breather's transmission amplitude.
Wednesday, 25 September 2013
13:00
Jeong-Hyuck Park (DAMTP, Cambridge/Sogang University, Seoul)
Preseminar for PhD students
14:30
Jeong-Hyuck Park (DAMTP, Cambridge/Sogang University, Seoul)
This talk aims to explain our recent construction of D=10 N=2 supersymmetric double field theory with 32 supersymmetries to the full order in fermions. The constructed action unifies type IIA and IIB supergravities in a manifestly covariant manner with respect to O(10,10) T-duality and a pair of local Lorentz groups, or Spin(1,9) \times Spin(9,1), besides the usual general covariance of supergravities. While the theory is unique, the solutions are twofold. Type IIA and IIB supergravities are identified as two different types of solutions rather than two different theories. Intriguingly, the spacetime coordinates are doubled yet gauged.