Triangle Seminars
Wednesday, 13 Jan 2010
M2-branes at hypersurface singularities and their deformations
📍 London
James Sparks
(Oxford)
A-field and B-field from Freed-Witten anomaly
Rafaelle Savelli
(SISSA)
Abstract:
Freed-Witten anomaly is a global ambiguity of the string path integral
measure in the presence of D-branes. It turns out it uniquely
determines,
by imposing its cancellation, the topological type of both the A and
the B
fields when restricted to the brane, as it naturally involves the
interplay between open and closed string degrees of freedom. After
introducing the suitable mathematical framework provided by the
theory of
gerbes with connections, I will try to characterize the nature of the
gauge bundle on a brane in the most general closed string background.
Furthermore, I will go over a case by case analysis, focusing on how it
can account for fractional RR and Page charges and showing the physical
relevance of the resulting K-theoretical improvement for classifying
D-brane charges.
Reference: L. Bonora, F. Ferrari Ruffino, R. S., arXiv: 0810.4291
Freed-Witten anomaly is a global ambiguity of the string path integral
measure in the presence of D-branes. It turns out it uniquely
determines,
by imposing its cancellation, the topological type of both the A and
the B
fields when restricted to the brane, as it naturally involves the
interplay between open and closed string degrees of freedom. After
introducing the suitable mathematical framework provided by the
theory of
gerbes with connections, I will try to characterize the nature of the
gauge bundle on a brane in the most general closed string background.
Furthermore, I will go over a case by case analysis, focusing on how it
can account for fractional RR and Page charges and showing the physical
relevance of the resulting K-theoretical improvement for classifying
D-brane charges.
Reference: L. Bonora, F. Ferrari Ruffino, R. S., arXiv: 0810.4291
Posted by: IC
Thursday, 14 Jan 2010
(Super)conformal Symmetry of Scattering Amplitudes in N=4 SYM
Niklas Beisert
(MPI, Potsdam)
Abstract:
Tremendous progress in computing perturbative scattering amplitudes
in N=4 supersymmetric gauge theory has been made over the past few
years. Importantly the planar amplitudes appear to display a dual
conformal invariance next to the usual conformal symmetry. Altogether
the symmetry enlarges to a Yangian algebra known from the context of
integrable models. This infinite-dimensional symmetry might have the
power to completely fix the S-matrix by algebraic means.
In this talk we review the above developments. We then discuss
conformal symmetry for tree and loop scattering amplitudes. It turns
out that the free conformal symmetry generators are anomalous which
calls for certain deformations to make the symmetries exact. These
relate amplitude with different numbers of legs, and thus they
contribute substantially to a complete algebraic determination.
Tremendous progress in computing perturbative scattering amplitudes
in N=4 supersymmetric gauge theory has been made over the past few
years. Importantly the planar amplitudes appear to display a dual
conformal invariance next to the usual conformal symmetry. Altogether
the symmetry enlarges to a Yangian algebra known from the context of
integrable models. This infinite-dimensional symmetry might have the
power to completely fix the S-matrix by algebraic means.
In this talk we review the above developments. We then discuss
conformal symmetry for tree and loop scattering amplitudes. It turns
out that the free conformal symmetry generators are anomalous which
calls for certain deformations to make the symmetries exact. These
relate amplitude with different numbers of legs, and thus they
contribute substantially to a complete algebraic determination.
Posted by: QMW
Sunday, 17 Jan 2010
Gradient formula for the beta function of 2d quantum field theory
Anatoly Konechny
(Heriot-Watt)
Abstract:
I will explain a gradient formula for beta functions of two-dimensional
quantum field theories. The gradient formula has the form derivative c = - (gij+Delta gij+bij) bj where bj are the beta functions, c and gij are the Zamolodchikov c-function and metric, bij is an antisymmetric tensor introduced by H. Osborn and Delta gij is a certain metric correction. The formula is derived under the assumption of stress-energy conservation and certain conditions on the infrared behaviour the most significant of which is the condition that the large distance limit of the field theory does not exhibit spontaneously broken global conformal symmetry. Being specialized to non-linear sigma models this formula implies a one-to-one correspondence between renormalization group fixed points and critical points of c.
I will explain a gradient formula for beta functions of two-dimensional
quantum field theories. The gradient formula has the form derivative c = - (gij+Delta gij+bij) bj where bj are the beta functions, c and gij are the Zamolodchikov c-function and metric, bij is an antisymmetric tensor introduced by H. Osborn and Delta gij is a certain metric correction. The formula is derived under the assumption of stress-energy conservation and certain conditions on the infrared behaviour the most significant of which is the condition that the large distance limit of the field theory does not exhibit spontaneously broken global conformal symmetry. Being specialized to non-linear sigma models this formula implies a one-to-one correspondence between renormalization group fixed points and critical points of c.
Posted by: IC