Black Holes and Supersymmetry Grantee: Armen Yeranayn Expiration of the Grant: 31 / 08 / 2017 Work Institution: Laboratori Nazionali di Frascati, INFN Scientific Supervisor: Prof. Augusto Sagnotti Roma, 2 March 2017

Black Holes and Supersymmetry Motivations of the project and background My current research aims at extending the study of component actions that emerge, in global and local Supersymmetry, when one or more supersymmetries are non-linearly realized. Non-linear realizations are naturally perceived as mere low-energy approximations, of interest in special limits where some particles become particularly heavy. However, in String Theory they seem to play a more fundamental role, in the presence of branes. Their very emergence actually seems to signal a deep incompleteness of our current formulation of String Theory. When Supersymmetry is broken, proceeding further within String Theory alone is fraught with difficulties that are both technical and conceptual, so that no clear progress was made for a long time. On the contrary, the low-energy Supergravity might hold the key for pinpointing the nature of these systems. Roma, 2 March 2017

Black Holes and Supersymmetry Motivations of the project and background An interesting intermediate step would concern Born-Infeld systems. Counterparts of these systems with different numbers of linearly and non-linearly realized supersymmetry ought to exist. The simplest Lagrangian of this type, the original Born-Infeld theory was introduced in the1930's. There is an upper bound on field strength, in analogy with the relativistic particle action. The existence of a limiting field strength can find a physical justification in the increasing pair production from vacuum (Bachas&Porrati 1992). Photonic solutions are very important for nonlinear optics. They pass through one another without scattering. Scalar BI Theory – non-linear theory with no shock-wave propagation. Roma, 2 March 2017

Motivations of the project and background Black Holes and Supersymmetry Motivations of the project and background The BI theory made a striking and unexpected comeback in String Theory, in the 1980's, when Fradkin and Tseytlin first linked it to the dynamics of open strings in a constant electromagnetic background. Other reason of interest on the BI theory, has to do with the partial breaking of supersymmetry. When completed by the addition of gaugino interactions, the BI model conceals indeed a second, non--linearly realized supersymmetry while μ defines the supersymmetry breaking scale. The lessons of Born-Infeld systems are profound, very instructive and still not fully transparent. These theories display a rich pattern of geometrical structures that, as we have stressed, might provide a useful starting point for illuminating some foundational aspects of String Theory that appear otherwise beyond reach. Roma, 2 March 2017

Black Holes and Supersymmetry Eventuale altro logo Synthesis of the results achieved in 2016 Systematic construction and study of analytical forms of Born-Infeld actions with two vector fields whose equations of motions invariant under U(1)xU(1), SU(2) and U(2). The case U(2) is only known implicitly, while all cases with lower duality symmetries (U(1), U(1) xU(1) and SU(2)) have been identified (strating from proper guesses). Some relevant progress was made recently… The standard Born-Infeld action has an equation of motion invariant under U(1) duality rotations, just like Maxwell e.m.: this means that the condition (Gaillard and Zumino1981) is satisfied. Two fields: now one can have at most invariance under U(2) rotations, which requires that the constitutive relations satisfy the conditions Roma, 2 March 2017

Black Holes and Supersymmetry Eventuale altro logo Synthesis of the results achieved in 2016 (Gaillard and Zumino1981) There are some intermediate cases, when only part of the equations are satisfied. The correspond to SU(2) (when only three equations are satisfied) or to U(1) X U(1) (when only two equations are satisfied) Important Point: in all these cases, due to the second equation (which has no analog for one field) a Lagrangian has a manifest U(1) symmetry Actions with the full U(n) duality group were proposed by Aschieri, Brace, Morariu, Zumino (2000), but they are not in closed form even for n=2. Roma, 2 March 2017

Black Holes and Supersymmetry Eventuale altro logo Synthesis of the results achieved in 2016 Using the master action approach we have constructed analytical expressions in all three cases (Ferrara, Sagnotti and A. Y., 2015 and 2016) Introducing complex combinations of field strengths, we have Roma, 2 March 2017

Black Holes and Supersymmetry Eventuale altro logo Synthesis of the results achieved in 2016 where Roma, 2 March 2017

Black Holes and Supersymmetry Eventuale altro logo Plan of activities 2017 – 2018 Possible generalizations of the approach to the U(n) case. In particular, construction and investigation of four-field actions which exhibit various types of dualities below the maximum U(4). Generalizations of the method applied for two fields using quaternions instead of complex variables? In the U(2) case , search for other simple analytical solutions. Analysis of point-like exact solutions of these models with extended duality. Construction of Hamiltonians for these systems and investigation a positivity of energy. Construction and detailed investigation of component actions with half of the supersymmetries broken in spaces with constant curvature, for instance de Sitter space. Detailed investigation of the connection of these models to Supergravity, with emphasis on cosmological models with one of more non-linearly realized supersymmetries. Roma, 2 March 2017

Black Holes and Supersymmetry Eventuale altro logo Possible links to other Projects (internal to Centro Fermi): B. L. Cerchiai: A geometric approach to quantum gravity A. Marrani: Quantum gravity: from black holes to quantum entanglement Possible participation to external Call for Projects: Bogoliubov Laboratory of Theoretical Physics, JINR, Russia Yerevan State University, Armenia Roma, 2 March 2017

Black Holes and Supersymmetry Eventuale altro logo THANK YOU! Roma, 2 March 2017