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Quantum field theory and supersymmetry

François Delduc, Marc Magro, Henning Samtleben

Field Theory

Topics studied in the group include: conformal and topological theories with boundary, in particular their geometrical aspects and applications (K. Gawedzki), supersymmetric field theories, in particular supergravity, Yang-Mills theory with extended supersymmetry, low-dimensional theories (F. Delduc, M. Magro, H. Samtleben).

String Theory

String theory is a theory to describe nature at the smallest length scales. It replaces the concept of point-like elementary particles or local fields by extended stringlike objects. It is at the heart of the unification of the different fundamental interactions and has had tremendous impact on our understanding of quantum field theories, gravitational interactions and geometry. Many research activities of our group are centered around various aspects and applications of this theory.

Conformal Field Theory

There has been a constant progress in two-dimensional quantum field theory stimulated by the applications to classical and quantum statistical mechanics, condensed matter and string theory. We have developed an original geometric approach to the WZW sigma models of conformal field theory, based on the geometry of gerbes and gerbe modules that permits to tackle the global aspects of conformal sigma models.

Supersymmetry

Supersymmetry is a symmetry that exchanges bosonic and fermionic degrees of freedom. It plays a prominent role in string theory and for the understanding of the structure of divergencies in quantum field theories. In particular, we study supersymmetric theories in low dimensions, including models of superconformal quantum mechanics.

Supergravity

At low energies and after compactification of the extra dimensions, string theory is described by effective field theories that combine gravity, supersymmetry and gauge symmetry, so-called gauged supergravities. Our research focusses on the construction and classification of these theories in various space-time dimensions and their applications to (non-geometric) flux compactifications. Modern developments in generalized and exceptional geometry provide powerful tools for the study of string compactifications.

AdS / CFT correspondence

The AdS / CFT correspondence is a conjectured holographic duality between particular four-dimensional superconformal gauge theories (CFT) and string theory on Anti-de Sitter (AdS) backgrounds. A well established example is the maximally supersymmetric case for which the gauge theory is N=4 super Yang-Mills theory. The integrability of the underlying models plays a key role in this correspondence. We investigate the algebraic properties underlying the classical integrability of the relevant non-linear sigma-models. Modern developments include the construction of integrable deformations of these sigma-models.

Selected Publications

  1. Green-Schwarz Mechanism for String Dualities, C. Eloy, O. Hohm, and H. Samtleben,  Phys. Rev. Lett. 124, 091601 (2020). [arXiv:1912.01700]

  2. Integrable coupled sigma-models, F. Delduc, S. Lacroix, M. Magro, and B. Vicedo, Phys. Rev. Lett. 122, 041601 (2019). [arXiv:1811.12316]

  3. Exceptional Form of D=11 Supergravity, O. Hohm and H. Samtleben, Phys. Rev. Lett.  111, 231601 (2013). [arXiv:1308.1673]

  4. Consistent Type IIB Reductions to Maximal 5D Supergravity, A. Baguet, O. Hohm and H. Samtleben, Phys. Rev. D 92,  065004 (2015). [arXiv:1506.01385]

  5. Integrable deformation of the AdS5 x S5 superstring action, F. Delduc, M. Magro and B. Vicedo, Phys. Rev. Lett.  112, 051601 (2014). [arXiv:1309.5850]