Triangle Seminars
Monday, 12 Nov 2007
Open/closed topological field theory and topological gravity
Ezra Getzler
Tuesday, 13 Nov 2007
Hedgehog black holes and the deconfinement transition
Matthew Headrick
(Stanford)
Models with a nontrivial metric in quantum mechanics
Miloslav Znojil
(Nuclear Physics Institute, Prague)
Abstract:
A not entirely formal discussion of some aspects of the so called PT-symmetric quantum mechanics will involve the following four more or less open problems:
1. What are chances of a closed-form description of boundaries of stability (i.e., of the allowed domain D of physical parameters) in a generic PT-symmetric model? (hint: we shall demonstrate that they are better than expected)
2. What happens if the coordinates are allowed to be topologically nontrivial? (hint: one gets the so called quantum toboggans)
3. Should and could a realistic PT-symmetric model be also based on a non-Hermitian form of the parity? (we intend to recommend it)
4. Could the use of a realistic PT-symmetric model be made compatible with a time-dependent metric? (we shall show how).
A not entirely formal discussion of some aspects of the so called PT-symmetric quantum mechanics will involve the following four more or less open problems:
1. What are chances of a closed-form description of boundaries of stability (i.e., of the allowed domain D of physical parameters) in a generic PT-symmetric model? (hint: we shall demonstrate that they are better than expected)
2. What happens if the coordinates are allowed to be topologically nontrivial? (hint: one gets the so called quantum toboggans)
3. Should and could a realistic PT-symmetric model be also based on a non-Hermitian form of the parity? (we intend to recommend it)
4. Could the use of a realistic PT-symmetric model be made compatible with a time-dependent metric? (we shall show how).
Posted by: KCL
On the Riemann-Hilbert-Birkhoff inverse monodromy problem and the asymptotic analysis of the third Painleve transcendents
David Niles
(Dijon)
Wednesday, 14 Nov 2007
Pohlmeyer reduction of the AdS5 x S5 superstring sigma model
Maxim Grigoriev
(Institute of Mathematical Sciences, Imperial College)
Abstract:
Motivated by a desire to find a useful 2d Lorentz-invariant reformulation of the AdS5 x S5 superstring world-sheet theory in terms of physical degrees of freedom we investigate a Pohlmeyer-reduced version of the corresponding supercoset sigma model. The Pohlmeyer reduction procedure involves several steps. Starting with a coset space string sigma model in the conformal gauge and writing the classical equations in terms of currents one can fix the residual conformal diffeomorphism symmetry and kappa-symmetry and introduce a new set of variables (related locally to currents but non-locally to the original string coordinate fields) so that the Virasoro constraints are automatically satisfied. The resulting gauge-fixed equations can be obtained from a Lagrangian of a non-abelian Toda type: a gauged WZW model with an integrable potential coupled also to a set of 2d fermionic fields. The final form of the Pohlmeyer-reduced theory can be found by integrating out the 2d gauge field of the gauged WZW model. Its small-fluctuation spectrum is that of 8 bosonic and 8 fermionic degrees of freedom with equal masses. We show that in the special case of the AdS2 x S2 superstring model the reduced theory is supersymmetric: it is equivalent to the (2,2) supersymmetric extension of the sine-Gordon model.
Motivated by a desire to find a useful 2d Lorentz-invariant reformulation of the AdS5 x S5 superstring world-sheet theory in terms of physical degrees of freedom we investigate a Pohlmeyer-reduced version of the corresponding supercoset sigma model. The Pohlmeyer reduction procedure involves several steps. Starting with a coset space string sigma model in the conformal gauge and writing the classical equations in terms of currents one can fix the residual conformal diffeomorphism symmetry and kappa-symmetry and introduce a new set of variables (related locally to currents but non-locally to the original string coordinate fields) so that the Virasoro constraints are automatically satisfied. The resulting gauge-fixed equations can be obtained from a Lagrangian of a non-abelian Toda type: a gauged WZW model with an integrable potential coupled also to a set of 2d fermionic fields. The final form of the Pohlmeyer-reduced theory can be found by integrating out the 2d gauge field of the gauged WZW model. Its small-fluctuation spectrum is that of 8 bosonic and 8 fermionic degrees of freedom with equal masses. We show that in the special case of the AdS2 x S2 superstring model the reduced theory is supersymmetric: it is equivalent to the (2,2) supersymmetric extension of the sine-Gordon model.
Posted by: IC
Small, medium and giant magnons
Gordon Semenoff
(University of British Columbia)
Abstract:
The spin chain analogy of the problem of computing conformal dimensions of compostie operators in N=4 super Yang-Mills theory and the idea that the theory and its string dual could be integrable and could perhaps be solved by a Bethe ansatz has attracted a lot of attention. The present view is that this should be done in two steps. First one must solve the asymptotic Bethe ansatz which should obtain the spectrum of infinitely large operators where the problem simplifies considerably, being posed as scattering of magnons with a factorized S-matrix. Subsequently a thermodynamic Bethe ansatz should be used to find the spectrum of finite size operators. An interesting window onto finite size effects is the giant magnon, the string dual of the spin chain magnon. The seminar will discuss the giant magnon solution of string theory and attempts to interpret its finite size effects as the spectrum of a single magnon on an orbifolded version of N=4 Yang-Mills theory with reduced supersymmetry.
The spin chain analogy of the problem of computing conformal dimensions of compostie operators in N=4 super Yang-Mills theory and the idea that the theory and its string dual could be integrable and could perhaps be solved by a Bethe ansatz has attracted a lot of attention. The present view is that this should be done in two steps. First one must solve the asymptotic Bethe ansatz which should obtain the spectrum of infinitely large operators where the problem simplifies considerably, being posed as scattering of magnons with a factorized S-matrix. Subsequently a thermodynamic Bethe ansatz should be used to find the spectrum of finite size operators. An interesting window onto finite size effects is the giant magnon, the string dual of the spin chain magnon. The seminar will discuss the giant magnon solution of string theory and attempts to interpret its finite size effects as the spectrum of a single magnon on an orbifolded version of N=4 Yang-Mills theory with reduced supersymmetry.
Posted by: KCL
Holographic Aspects of Generalized Electric-Magnetic Duality
Anastasios Petkou
(University of Crete)
Friday, 16 Nov 2007
Heavy Ion Collisions and AdS/CFT
Amos Yarom
(LMU, Munich)
Abstract:
Heavy-ion collision experiments manage to probe the quark-gluon plasma of QCD. The plasma created is strongly coupled and is difficult to analyze using conventional means. In this talk, we shall use the AdS/CFT correspondence to study properties of particles moving through a quark-gluon plasma. Such probe particles provide a model for understanding several unanswered puzzles exhibited by the experiment.
Heavy-ion collision experiments manage to probe the quark-gluon plasma of QCD. The plasma created is strongly coupled and is difficult to analyze using conventional means. In this talk, we shall use the AdS/CFT correspondence to study properties of particles moving through a quark-gluon plasma. Such probe particles provide a model for understanding several unanswered puzzles exhibited by the experiment.
Posted by: IC