## Past seminars

### Academic year: September 2005 - September 2006

Place:  Leuven, Celestijnenlaan 200D 06.34
Time:    Friday, June 2, 2006 at 10:30
Place:  VUB/ULB, Campus Plaine, building NO, 5th floor, Salle Solvay
Time:   Wednesday, May 31, 2006, 10:30-13:30

The first goal of these lectures is to collect and explain the ingredients required to formulate the basic N=1 supergravity in 4 spacetime dimensions which describes the graviton and gravitino. The ingredients include the Rarita-Schwinger field, Majorana spinors, and the differential geometry of torsion. We will then prove in detail that the supergravity action is invariant under local supersymmetry principles. After that we will consider some applications of supergravity. Depending on the time available and the interest of students these might include the Witten-Nester positive energy proof, anti-de Sitter supergravity and some aspects of the AdS/CFT correspondence, and new research on a version of supergravity in which the physics in local frames is invariant under the SIM(2) subgroup of the Lorentz group rather than the full group.

Outline of first day, background ideas and tools for supergravity.

1. Gauge principles and degrees of freedom (d.o.f)
2. The Maxwell field in D spacetime dimensions-- (D-2) d.o. f.
3. General coordinate invariance and the gravitational field--
i. The Linearized Ricci tensor
ii. The gravitational field has (D^2 - 3D)/2 d.o.f
4. Spinor and Majorana spinor fields
5. Global SUSY --- The conserved supercurrent of super-Yang-Mills theory. The N=1 SUSY algebra and its massless representations.
6. The free gravitino field
i. the Lagrangian and different forms of the equation of motion.
ii. counting degrees of freedom -- (1/2)(D-3)2^[D/2]
iii. the propagator
iv. inconsistent electromagnetic interactions
7. Review of differential geometry
i. the metric and frames, local Lorentz invariance
ii. spin connection, torsion, first Cartan structure equation
iii. curvature and the second structure equation
iv. Bianchi and Ricci identities
8. The Dirac Lagrangian in curved space-time

Place:  Leuven, Celestijnenlaan 200D 06.34
Time:   Wednesday, May 24, 2006, 10:30-13:30

Place:  VUB/ULB, Campus Plaine, building NO, 5th floor, Salle Solvay
Time:   Wednesday, May 17, 2006 at 10:30

We will discuss the issue of classifying all supersymmetric solutions of supergravity and string theory. Such classifications have been obtained for theories with few supersymmetries but not for maximal supergravity. To this end, a new method called spinorial geometry has been proposed. We will review it and illustrate its efficiency by recent progress in the IIB case.

Place:  VUB/ULB, Campus Plaine, building NO, 5th floor, Salle Solvay
Time:   Wednesday, May 17, 2006 at 10:30

Well understood examples of the gauge/string correspondence (AdS/CFT) arise from putting branes at singularities. In particular four-dimensional N=1 superconformal gauge are engineered putting D3 branes at the tip of Calabi-Yau cones. We discuss new explicit constructions of Calabi-Yau cones and of their dual gauge theories. We then show how generic, exact, checks of AdS/CFT are possible, within various "protected sectors" of the correspondence, such as BPS objects or Chern-Simons couplings/triangle anomalies.

Place:  Leuven, Celestijnenlaan 200D 06.34
Time:   Wednesday, May 10, 2006 at 13:30

The Tits-Satake projection of non maximally split real sections of simple Lie algebras is well known in mathematics. In this talk we will review how this projection works and how it is related to the concept of paint group. We will indicate how one can extend this projection to all solvable Lie algebras entering the classification of homogeneous special geometries, relevant to supergravity theories with 8 supercharges. Finally, we show that supergravity models with 8 supercharges and a homogeneous scalar manifold can be grouped in a small number of universality classes, capturing for instance some essential features of their dynamics.

Place:  Leuven, Celestijnenlaan 200D 06.34
Time:   Wednesday, May 10, 2006 at 10:30

Place:  ULB/VUB, Campus Plaine, building NO, 5th floor, Salle Solvay
Time:   Wednesday, May 3, 2006 at 13:30

I will talk about the gravitational dual description of Wilson loop operators in SYM theories. In particular, I will show that all half- BPS Wilson loops in N=4 SYM (which are labeled by Young tableaus) can be described in terms of D5-branes or alternatively in terms of D3- branes in AdS_5xS_5.

Place:  VUB/ULB, Campus Plaine, building NO, 5th floor, Salle Solvay
Time:   Wednesday, May 3, 2006 at 10:30

I will discuss some recent developments concerning supersymmetry of type IIA, IIB and type I in ten dimensions. In particular, I will talk about the discovery of 10-form gauge potentials, and 1/2 BPS nine-branes which couple to them.

Place:  Leuven, Celestijnenlaan 200D 06.34
Time:   Wednesday, April 26, 2006 at 13:30

I will introduce singleton representations and discuss their relevance to the study of strings and branes in AdS. In the tensionless limit, extended objects exhibit a partonic behaviour and, for large spin, world-volume solitons can be effectively described by a multi-singleton system. This led to the proposal that a discretized tensionless brane with N constituents in D-dimensional AdS is described by a singleton-gas worldline sigma model. I will discuss in detail a gauged WZW model on a 2(D-1)-dimensional target (phase-) space, describing these singletonic degrees of freedom when the continuum limit on the number of brane constituents is taken.

Place:  Leuven, Celestijnenlaan 200D 06.34
Time:   Wednesday, April 26, 2006 at 10:30

Place:  ULB/VUB, Campus Plaine, building NO, 5th floor, Salle Solvay
Time:   Wednesday, April 19, 2006 at 13:30

Recently, Ribault and Teschner have proven that the string scattering amplitudes in AdS3 space can be fully described in terms of correlation functions in a different theory: The Liouville field theory. This turns out to be a fruitful tool to work out the details of string theory in non-compact curved spacetimes by making use of the "better understood" Liouville theory. In this talk, I will describe how such a connection between both theories is related with another map between a pair of CFTs; namely, the Fateev-Zamolodchikov-Zamolodchikov conjecture, which relates the string theory on 2D black holes with the often called sine-Liouville field theory. Other applications, as the explicit computations of correlation functions will be discussed as well.

Bibliography: This regards the results of hep-th/0511252.

Place:  Leuven, Celestijnenlaan 200D 06.34
Time:   Wednesday, April 5, 2006 at 13:30

In this talk I show how to formulate SU(N) gauge theories on a canonical noncommutative spacetime. It will then be shown that these actions are invariant under noncommutative Lorentz transformations. The quantization of these models will be briefly discussed as well as the bounds on spacetime noncommutativity. I then show that unimodular gravity can be implemented on such spaces and discuss the connection to the cosmological constant.

Place:  ULB/VUB, Campus Plaine, building NO, 5th floor, Salle Solvay
Time:   Wednesday, March 29, 2006 at 13:30

I will discuss the application of Generalised Complex Geometry to string compactifications and in particular to the analysis of the supergravity backgrounds dual to supersymmetric gauge theories

Place:  VUB/ULB, Campus Plaine, building NO, 5th floor, Salle Solvay
Time:   Wednesday, March 29, 2006 at 10:30

We discuss properties of 2 and 5 branes i 7 dimensions that are of relevance for topological M-theory. For the latter case this leads to a Calabi-Yau-filling brane in topological string theory which we interprete as a Kodaira-Spencer NS5-brane in the A-model.

Place:  Leuven, Celestijnenlaan 200D 06.34
Time:   Wednesday, March 22, 2006 at 13:30

Place:  Leuven, Celestijnenlaan 200D 06.34
Time:   Wednesday, March 22, 2006 at 10:30

In this talk I'll discuss some general features of D-branes in a general class of "D-calibrated" Type II backgrounds preserving four-dimensional N=1 supersymmetry. In particular, I'll present the general form of the superpotentials and D-terms governing space-time filling D-branes. The relation of superpotentials and D-terms with BPS domain walls and cosmic strings respectively will be also discussed in the geometrical framework provided by D-branes.

Place:  ULB/VUB, Campus Plaine, building NO, 5th floor, Salle Solvay
Time:   Wednesday, March 15, 2006 at 13:30

When T-duality is applied to time-like circles, the dual theory does not necessarily live on a time-like circle, and the overall space-time signature can change. We give a set of simple rules allowing one to determine the possible space-time signatures easily. The allowed patterns are reproduced by Triple-extended algebras's, but only after taking into account that the proper representation of Poincar duality on the algebra leads to a constraint. This constraint is exhibited, and some consequences are discussed.

Place:  VUB/ULB, Campus Plaine, building NO, 5th floor, Salle Solvay
Time:   Wednesday, March 15, 2006 at 10:30

It is shown that the family of 1/2-BPS states of N=4 SYM, giving rise to LLM droplet geometries, is in one to one correspondence with a family of classical solutions (D3 branes) of Vacuum String Field Theory, with a B-field playing the role of the inverse Planck constant of the droplet fermion system. The correspondence is established by relating the Wigner distribution of the N-fermions systems representing 1/2 BPS states, to low energy space profiles of stacks of VSFT D-branes. In this context the Pauli/Stringy exclusion principle appears as a consequence of the VSFT projector equation. It is observed that, at least in the 1/2 BPS sector (frozen D-branes moduli), OSFT on N D3 branes in flat space accounts for the dynamics of N giant gravitons probing (and backreacting on) a very highly curved AdS geometry.

Place:  ULB/VUB, Campus Plaine, building NO, 5th floor, Salle Solvay
Time:   Wednesday, March 8, 2006 at 13:30

I will cover three topics:
1. The computational complexity of the landscape, in particular the NP-completeness of the problem of finding Bousso-Polchinski flux vacua within a certain parameter range.
2. How techniques originally developed to count flux vacua in the landscape can be used to count black hole microstates, proving the Ooguri-Strominger-Vafa (OSV) conjecture in a particular limit.
3. A physics derivation of a refined version of the general OSV conjecture, based on S-duality and the black hole "molecule" representation of sparsely fluxed D4-branes.

Place:  VUB/ULB, Campus Plaine, building NO, 5th floor, Salle Solvay
Time:   Wednesday, March 8, 2006 at 10:30

We present supergravity solutions that describe cosmologies with AdS boundary conditions. We also describe the AdS/CFT dual field theory evolution of these solutions, and discuss what we can learn from this about the quantum nature of cosmological singularities.

Place:  Leuven, Celestijnenlaan 200D 06.34
Time:   Wednesday, March 1, 2006 at 13:30

I will demonstrate how to use the Mathematica package GAMMA (hep-th/0105086) to compute gamma matrix algebra and Fierz identities. After a general introduction to the most common functions in GAMMA I will turn to some explicit examples in 10 and 11 dimensional supergravity. GAMMA if freeware and can be downloaded from www.gran.name.

Place:  Leuven, Celestijnenlaan 200D 06.34
Time:   Wednesday, March 1, 2006 at 10:30

We describe systems of D3-branes at singularities in the presence of fractional branes, and their corresponding dual supergravity warped throats. The corresponding gauge theories have an RG evolution leading to cascades of Seiberg dualities, and to strong coupling phenomena in the infrared, like (partial) confinement, or generation of a superpotential removing the supersymmetric vacuum. The different behaviours are characterized by different geometric properties of the singularities at which the D3-branes sit.

Place:  ULB/VUB, Campus Plaine, building NO, 5th floor, Salle Solvay
Time:   Wednesday, February 22, 2006 at 13:30

We review the construction of a novel formulation of supergravity coupled to antisymmetric tensor fields and scalar fields with non-abelian gauge symmetry, in which the minimal couplings involve not only the electric vector fields but also their magnetic duals.The equations of motion and Bianchi identities are manifestly invariant with respect to the full global symmetry group of the ungauged theory without tensor fields. Applications of the model to String/M-theory compactifications are discussed.

Place:  VUB/ULB, Campus Plaine, building NO, 5th floor, Salle Solvay
Time:   Wednesday, February 22, 2006 at 10:30

Straightforward evaluation of the correlation functions in 2D minimal�gravity�requires integration over the moduli space. For degenerate fields the�higher�equations of motion of the Liouville field theory allow to turn the�integrand�to a derivative and to reduce it to the boundary terms and the so-called�curvature contribution. The last is directly related to the expectation�value�of the corresponding ground ring element. The action of this element on a�cohomology related to a generic matter primary field is evaluated directly�through the operator product expansions of the degenerate fields. This�permits�us to construct the ground ring algebra and to evaluate the curvature term�in�the four-point function. The operator product expansions of the Liouville�logarithmic primaries'' are also analyzed and relevant logarithmic terms�are�carried out. All this results in an explicit expression for the four-point�correlation number of one degenerate and three generic matter fields. We�compare this integral with the numbers coming from the matrix models of 2D�gravity and discuss some related problems and ambiguities.

(based on hep-th/0510214)

Place:  Leuven, Celestijnenlaan 200D 06.34
Time:   Wednesday, February 15, 2006 at 13:30

We will review recent developments in topological membrane theory of cohomological type. In particular we will discuss the formulation of a topological membrane theory on manifolds with G2 structure and its role in the topological M-theory picture.

[There will also be 2 preliminary lectures on Tuesday 14/2 in the local ULB Group seminars.]

Place:  Leuven, Celestijnenlaan 200D 06.34
Time:   Wednesday, February 15, 2006 at 10:30

Using the connection between the strong coupling limit of type II superstring and M-theory, the structure of the derivative expansion of IIB and IIA effective action can be extracted from the four-graviton multiloop amplitude in eleven dimensions. This expansion gives an infinite set of non- renormalisation theorems for type IIB superstring and strong constraints on the behaviour of multiloop superstring amplitude in type IIA. We will discuss how these result can give some important information about the structure of superstring multiloop amplitude at high-genus.

Place:  ULB/VUB, Campus Plaine, building NO, 5th floor, Salle Solvay
Time:   Wednesday, February 8, 2006 at 13:30

After a short review of the G�del solution in 2+1 gravity, I show it can be viewed as a solution of the Einstein-Maxwell theory with a negative cosmological constant and a Chern-Simons term. Particles and black holes will then be constructed by means of identifications and a general solution will be displayed. Conserved charges and thermodynamics of the solutions will be discussed in detail.

(based on hep-th/0512105)

Place:  VUB/ULB, Campus Plaine, building NO, 5th floor, Salle Solvay
Time:   Wednesday, January 25, 2006 at 10:30

Place:  Leuven, Celestijnenlaan 200D 06.32
Time:   Thursday, December 22, 2005 at 13:30

In N=1 supergravity and N=2 susy, constant Fayet Iliopoulos (FI) terms are useful to construct potentials for cosmic strings and inflation models. However, there is a no go theorem for FI terms in N=2 supergravity. Recently we have found a way to go around the no-go theorem and we constructed the first example of half- BPS cosmic string from N=2 supergravity. I will first review that construction. I will then comment on how it can be extended to obtain de Sitter space and other cosmologically interesting features from N=2 supergravity.

Place:  Leuven, Celestijnenlaan 200C 01.10
Time:   Thursday, December 22, 2005 at 10:30

After a short overview of BTZ black holes, I will stress some interesting geometric properties that some of them exhibit. I will then introduce the concept of (strict) deformation quantization, and show how the geometric features of BTZ black holes allow to deform them into non-commutative ones. I will end up by sketching the relation between string theory and non-commutative geometry in the flat case, and discuss the possible generalization to string theory on BTZ black holes via the Wess-Zumino-Witten model.

Place:  VUB/ULB, Campus Plaine, building NO, 5th floor, Salle Solvay
Time:   Thursday, December 15, 2005 at 13:30

In this talk, I will consider the problem of adding interactions to a free theory. I will present the field-antifield formalism, which offers a perfect frame for the classification of the local interactions that can be introduced perturbatively and consistently. I will illustrate this on the examples of exotic spin-2 fields and spin-3 fields.

Place:  ULB/VUB, Campus Plaine, building NO, 5th floor, Salle Solvay
Time:   Thursday, December 15, 2005 at 10:30

Place:  Leuven, Celestijnenlaan 200F 03.12
Time:   Thursday, December 8, 2005 at 13:30
Place:  Leuven, Celestijnenlaan 200C 01.10
Time:   Thursday, December 8, 2005 at 10:30

Based on hep-th/0503024

Place:  VUB/ULB, Campus Plaine, building NO, 5th floor, Salle Solvay
Time:   Thursday, November 24, 2005 at 13:30

The formulation of the non-linear sigma model in terms of flatconnection allows to derive a local functional equation encoding theinvariance of the Haar measure in the path-integral under local left multiplication. The local functional equation requires the introduction of the sources $J_\mu$, coupled to the flat connection $F_\mu$, and $K_0$, coupled to the composite operator $\phi_0$ (the constraint of the non-linear sigma model). We prove the validity of a weak power-counting theorem in the following form: although the number of divergent amplitudes is infinite only a finite number of divergent amplitudes have to be computed. The proof uses the linearized functional equation of which we provide the general solution in terms of local functionals. The counterterms are given in terms of linear combinations of these invariants and the coefficients are fixed by a finite number of divergent amplitudes. The latter contain only insertions of the composite operators $\phi_0$ and $F_\mu$. These amplitudes are at the top of a hierarchy implicit in the functional equation. As an example we derive the full set of counterterms at one-loop level. The renormalization of the local functional equation at the two-loop level is also addressed.

Place:  ULB/VUB, Campus Plaine, building NO, 5th floor, Salle Solvay
Time:   Thursday, November 24, 2005 at 10:30

Witten's topological B-model on the supertwistor space CP^3/4, and the alternative formulation of this twistor string due to Berkovits, describe perturbative tree amplitudes in N=4 Super Yang-Mills. Berkovits and Witten further showed that, beyond tree level, conformal supergravity modes are unavoidably mixed in with the gauge theory ones. This limits the usefulness of their models. After reviewing these developments, I will explore the possibility of defining a new twistor string which describes Einstein supergravity coupled to Super Yang-Mills theory, and present some evidence for its existence from a consideration of the perturbation theory of Siegel's chiral formulation of gravity.

Place:  Leuven, Celestijnenlaan 200D 06.32
Time:   Thursday, November 17, 2005 at 13:30

Place:  Leuven, Celestijnenlaan 200C 01.10
Time:   Thursday, November 17, 2005 at 10:30

Exact analytic solutions of supergravity, that can be constructed on the low dimensional (D<4) level, allow to study smooth realizations of the cosmological billiard phenomenon. The billiard is represented by a series of smooth bounces of metric scale factors and dilatons on axion walls that have bell-shaped behaviuor around bouncing times. In the case of non maximally split U-duality algebras there are present degenerate walls, and the axions realizing the same wall can be permuted by a compact subgroup of global isometries that we call "paint group".
Related papers: hep-th/0507256, hep-th/0507249, hep-th/0309237

Place:  VUB/ULB, Campus Plaine, building NO, 5th floor, Salle Solvay
Time:   Thursday, November 10, 2005 at 13:30

An S-duality invariant four dimensional string effective action will be considered to discuss axion-dilaton string cosmology. The classical solution will be discussed. The solution of the Wheeler-de Witt equation will be presented where S-duality invariance of the action plays a key role.

Place:  ULB/VUB, Campus Plaine, building NO, 5th floor, Salle Solvay
Time:   Thursday, November 10, 2005 at 10:30

[Alternative title: Ghosts and Temporal Photons Celebrate Halloween in the Rindler Wedge (without killing each other)]

The most naive extension of the Unruh effect to Feynmann gauge QED implies that a physical state as seen by a Minkowski observer is a density matrix containing some negative norm states as seen by a continually accelerating observer. One possibile explanation is an incompatibility of Unruh's trace and gauge invariance. Potential cures are discussed, such as a second physical state condition on the Rindler wedge and also a quantum correction to the Hamiltonian that eliminates the Rindler wedge as a solution.

Place:  Leuven, Celestijnenlaan 200D 06.32
Time:   Thursday, November 3, 2005 at 13:30

Place:  Leuven, Celestijnenlaan 200C 01.10
Time:   Thursday, November 3, 2005 at 10:30
Place:  VUB/ULB, Campus Plaine, building NO, 5th floor, Salle Solvay
Time:   Thursday, October 27, 2005 at 13:30
Place:  ULB/VUB, Campus Plaine, building NO, 5th floor, Salle Solvay
Time:   Thursday, October 27, 2005 at 10:30

Place:  Leuven, Celestijnenlaan 200F 03.12
Time:   Thursday, October 20, 2005 at 13:30

Place:  Leuven, Celestijnenlaan 200C 01.10
Time:   Thursday, October 20, 2005 at 10:30

Place:  VUB, Oefenplein, building G, 1G.012
Time:   Thursday, October 13, 2005 at 13:00

Place:  ULB, Campus Plaine, building NO, 5th floor, Salle Solvay
Time:   Thursday, October 13, 2005 at 10:30

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