Final Report Summary - SUPERFIELDS (SUPERSYMMETRY, QUANTUM GRAVITY AND GAUGE FIELDS)
The SUPERFIELDS Grant lasted 67 months and was devoted to the related themes of Supersymmetry, Quantum Gravity and Gauge Fields. The project was originally meant to unfold along three main lines:
1. black holes and attractors,
2. supersymmetry breaking and moduli stabilization,
3. higher-spin gauge fields.
A seven-month extension was motivated by novel activities related to early Universe Cosmology and Supersymmetry breaking in Supergravity. The results obtained comprise about 200 publications in main Scientific Journals, Conference Proceedings and Books, about a fourth of which were co-authored by two or more Team Members and Fellows.
Supersymmetry, a symmetry relating bosons and fermions, is a possible invariance both in local Quantum Field Theory and in theories of extended objects such as String Theory that first surfaced in the 1970’s. Supersymmetry determines a modification of gravity, known as Supergravity, whose first version was discovered in 1976 by D.Z. Freedman of MIT, P. van Nieuwenhuizen of the C.N. Yang Institute of Theoretical Physics at Stony Brook and the PI. These remarkable theories have been widely investigated during the last four decades, both in their own right and as low-energy limits of String Theory. They might well lie at the heart of the spontaneous breaking mechanism at work in the Standard Model of Electroweak interactions. Moreover, Supersymmetry provides a rationale for the dark matter that apparently permeates our Universe, and recent developments in observational Cosmology have boosted the interest in Supergravity models of inflation, which could have played a key role in the early stages of our Universe.
The Team obtained a number of general results on Black Holes in Supergravity (charge orbits, dualities, formal relations to entangled systems, extensions of the attractor mechanism discovered in 1995 by R. Kallosh of Stanford University, A. Strominger of Harvard University and the PI to non-supersymmetric systems). Several aspects of Black Holes and attractors were investigated:
• the classification of their orbits, quantum corrections to the Bekenstein-Hawking entropy in extended Supergravity, the first-order formalism for non-BPS black-hole flows based on the notion of a “fake superpotential” previously introduced by members of this team, stability properties of multi-center black holes and their split attractor flows (PI, S. Bellucci, A. Ceresole, G. Dall’Agata);
• extremal black holes in a non-perturbative completion of N=8 Supergravity were connected to its possible perturbative finiteness (PI, M. Bianchi);
• black-hole inspired techniques were also used to classify four-dimensional AdS vacua (GDA).
Supergravity entails important non-perturbative effects captured by instantons and wrapped branes, peculiar extended objects that are ubiquitous in String Theory. Their rich structure also encompasses extremal black holes and largely explains their dynamics. The initial part of the project was largely devoted to these themes, and we proceeded along the following lines:
• non-perturbative effects in superstring constructions were analyzed both as a way to develop a stringy instanton calculus and in connection to transitions among intersecting-brane vacua (MB, J. Morales);
• the excitations allowed in classically stable non-supersymmetric string vacua were linked to the Riemann zeta-function, and a manifestly T-duality invariant technique for evaluating one-loop modular integrals was developed (C. Angelantonj).
The ultimate nature of String Theory remains elusive, but both the high-energy behavior of string amplitudes and the AdS/CFT correspondence point to the possible role of huge symmetries that control higher-spin field theories, of which strings could be a particular realization. In a wider sense, these studies aim at quantifying long-held expectations that String Theory is a broken phase of a higher-spin theory, possibly of a rather special type. A number of results were obtained on these systems:
• cubic higher-spin vertices were derived systematically from massive string amplitudes in the tensionless limit (A. Sagnotti);
• the Fierz-Pauli program was brought to completion, providing general action principles for free Fermi fields of mixed symmetry (AS);
• the link between causal propagation in external fields and non-minimal higher-spin couplings was clarified (AS, M. Porrati);
• in the AdS/CFT context, boundary effects pointing to the breaking of higher-spin symmetries in the Vasiliev model were highlighted (PI, MP);
• properties of stable higher-spin states of superstring spectra were investigated (MB).
As we have anticipated, a fourth line related to Early Universe Cosmology received much attention during the last part of the project, and in particular during the final seven-month extension. Our key results were the following:
• a string-inspired supersymmetry breaking mechanism that could have injected the inflationary phase of our Universe was proposed and its links to the first CMB multipoles were investigated (AS);
• low-energy constraints reflecting the stability of the inflaton potential were derived, and the minimal supergravity embedding of the Starobinsky model of inflation, which rests on non-linear realizations, was proposed. This result boosted the interest in this type of constructions, and was followed world-wide by several investigations of partial supersymmetry breaking and super-Higgs effect in the inflationary phase. This also led to attempts to obtain realistic models for the exit from inflation, which would eventually connect this phase to the Standard Model of Particle Physics (PI, MP, AS).
More details can be found in the project web site: http://superfields.web.cern.ch/Superfields/
1. black holes and attractors,
2. supersymmetry breaking and moduli stabilization,
3. higher-spin gauge fields.
A seven-month extension was motivated by novel activities related to early Universe Cosmology and Supersymmetry breaking in Supergravity. The results obtained comprise about 200 publications in main Scientific Journals, Conference Proceedings and Books, about a fourth of which were co-authored by two or more Team Members and Fellows.
Supersymmetry, a symmetry relating bosons and fermions, is a possible invariance both in local Quantum Field Theory and in theories of extended objects such as String Theory that first surfaced in the 1970’s. Supersymmetry determines a modification of gravity, known as Supergravity, whose first version was discovered in 1976 by D.Z. Freedman of MIT, P. van Nieuwenhuizen of the C.N. Yang Institute of Theoretical Physics at Stony Brook and the PI. These remarkable theories have been widely investigated during the last four decades, both in their own right and as low-energy limits of String Theory. They might well lie at the heart of the spontaneous breaking mechanism at work in the Standard Model of Electroweak interactions. Moreover, Supersymmetry provides a rationale for the dark matter that apparently permeates our Universe, and recent developments in observational Cosmology have boosted the interest in Supergravity models of inflation, which could have played a key role in the early stages of our Universe.
The Team obtained a number of general results on Black Holes in Supergravity (charge orbits, dualities, formal relations to entangled systems, extensions of the attractor mechanism discovered in 1995 by R. Kallosh of Stanford University, A. Strominger of Harvard University and the PI to non-supersymmetric systems). Several aspects of Black Holes and attractors were investigated:
• the classification of their orbits, quantum corrections to the Bekenstein-Hawking entropy in extended Supergravity, the first-order formalism for non-BPS black-hole flows based on the notion of a “fake superpotential” previously introduced by members of this team, stability properties of multi-center black holes and their split attractor flows (PI, S. Bellucci, A. Ceresole, G. Dall’Agata);
• extremal black holes in a non-perturbative completion of N=8 Supergravity were connected to its possible perturbative finiteness (PI, M. Bianchi);
• black-hole inspired techniques were also used to classify four-dimensional AdS vacua (GDA).
Supergravity entails important non-perturbative effects captured by instantons and wrapped branes, peculiar extended objects that are ubiquitous in String Theory. Their rich structure also encompasses extremal black holes and largely explains their dynamics. The initial part of the project was largely devoted to these themes, and we proceeded along the following lines:
• non-perturbative effects in superstring constructions were analyzed both as a way to develop a stringy instanton calculus and in connection to transitions among intersecting-brane vacua (MB, J. Morales);
• the excitations allowed in classically stable non-supersymmetric string vacua were linked to the Riemann zeta-function, and a manifestly T-duality invariant technique for evaluating one-loop modular integrals was developed (C. Angelantonj).
The ultimate nature of String Theory remains elusive, but both the high-energy behavior of string amplitudes and the AdS/CFT correspondence point to the possible role of huge symmetries that control higher-spin field theories, of which strings could be a particular realization. In a wider sense, these studies aim at quantifying long-held expectations that String Theory is a broken phase of a higher-spin theory, possibly of a rather special type. A number of results were obtained on these systems:
• cubic higher-spin vertices were derived systematically from massive string amplitudes in the tensionless limit (A. Sagnotti);
• the Fierz-Pauli program was brought to completion, providing general action principles for free Fermi fields of mixed symmetry (AS);
• the link between causal propagation in external fields and non-minimal higher-spin couplings was clarified (AS, M. Porrati);
• in the AdS/CFT context, boundary effects pointing to the breaking of higher-spin symmetries in the Vasiliev model were highlighted (PI, MP);
• properties of stable higher-spin states of superstring spectra were investigated (MB).
As we have anticipated, a fourth line related to Early Universe Cosmology received much attention during the last part of the project, and in particular during the final seven-month extension. Our key results were the following:
• a string-inspired supersymmetry breaking mechanism that could have injected the inflationary phase of our Universe was proposed and its links to the first CMB multipoles were investigated (AS);
• low-energy constraints reflecting the stability of the inflaton potential were derived, and the minimal supergravity embedding of the Starobinsky model of inflation, which rests on non-linear realizations, was proposed. This result boosted the interest in this type of constructions, and was followed world-wide by several investigations of partial supersymmetry breaking and super-Higgs effect in the inflationary phase. This also led to attempts to obtain realistic models for the exit from inflation, which would eventually connect this phase to the Standard Model of Particle Physics (PI, MP, AS).
More details can be found in the project web site: http://superfields.web.cern.ch/Superfields/