Asymptotic symmetries at null-infinity for the Rarita–Schwinger field with magnetic term

Funder: Cambridge Trust; doi: https://doi.org/10.13039/501100003343Funder: King’s College Cambridge, University of Cambridge; doi: https://doi.org/10.13039/501100000648Abstract In this paper we study the magnetic charges of the free massless Rarita–Schwinger field in four dimensional asymptotically flat space-time. This is the first step towards extending the study of the dual BMS charges to supergravity. The magnetic charges appear due to the addition of a boundary term in the action. This term is similar to the theta term in Yang–Mills theory. At null-infinity an infinite dimensional algebra is discovered, both for the electric and magnetic charge.</jats:p

Phase Space Renormalization and Finite BMS Charges in Six Dimensions

We perform a complete and systematic analysis of the solution space of six-dimensional Einstein gravity. We show that a particular subclass of solutions -- those that are analytic near $\mathcal{I}^+$ -- admit a non-trivial action of the generalised Bondi-Metzner-van der Burg-Sachs (GBMS) group which contains \emph{infinite-dimensional} supertranslations and superrotations. The latter consists of all smooth volume-preserving Diff$\times$Weyl transformations of the celestial $S^4$. Using the covariant phase space formalism and a new technique which we develop in this paper (phase space renormalization), we are able to renormalize the symplectic potential using counterterms which are \emph{local} and \emph{covariant}. We then construct charges which faithfully represent the GBMS algebra and in doing so, settle a long-standing open question regarding the existence of GBMS symmetries in higher dimensional non-linear gravity. Finally, we show that the semi-classical Ward identities for the supertranslations and superrotations are precisely the leading and subleading soft-graviton theorems respectively.Comment: 75 pages, 1 figur

Magnetic charges and phase space renormalization of gravity

In the first part of this thesis we perform a complete and systematic analysis of the solution space of six-dimensional Einstein gravity. We show that a particular subclass of solutions – those that are analytic near I+ – admit a non-trivial action of the generalised Bondi-Metzner-van der Burg- Sachs (GBMS) group which contains infinite-dimensional supertranslations and superrotations. The latter consists of all smooth volume-preserving Diff×Weyl transformations of the celestial S4. Using the covariant phase space formalism and a new technique which we present in this thesis (phase space renormalization), we are able to renormalize the symplectic potential using counterterms which are local and covariant. The Hamiltonian charges corresponding to GBMS diffeomorphisms are non-integrable. We show that the integrable part of these charges faithfully represent the GBMS algebra and in doing so, settle a long-standing open question regarding the existence of infinite-dimensional asymptotic symmetries in higher even dimensional non-linear gravity. In the second part of this thesis, we study the dual charges of N = 1 supergravity in asymptotically flat spacetime. The action considered is the usual supergravity action with a topological contribution. This is the Nieh-Yan term and the magnetic term of the free Rarita-Schwinger field. Through methods of the covariant phase space formalism we construct the charges conjugate to supersymmetry, diffeomorphism and Lorentz transformations. The additional term in the action will lead to new, non-vanishing contributions to these charges. The magnetic diffeomorphism charges are equivalent to the ones previously found for gravity, while the dual supersymmetric charges are new and do not appear for the free Rarita-Schwinger field. We find that the asymptotic symmetry group for supergravity can only include global conformal transformations on the celestial sphere

Market Failures in the Area of Art (The Case of Performing Arts)

Market failures in the field of performing arts are determined by their nature and technical features. In this case the term “quasi market failures” has been introduced in order to represent more precisely this atypical situation. Arts possess positive external effects of the nature of common benefits, i.e. pure public goods – common consumption without exclusion. The effects are internalized by subsidizing. The market of performing art is incomplete. There is an information asymmetry between demand and supply. The analyzed market defects complete their characteristics as a weak market subject and are a substantial evidence of state intervention and regulation of the sector.

Magnetic charges in supergravity

Abstract In this paper we study the dual charges of $$\mathcal{N}$$ N = 1 supergravity in asymptotically flat space-time. The action considered is the usual supergravity action with a topological contribution. This is the Nieh-Yan term and the magnetic term of the free Rarita-Schwinger field. Through methods of the covariant phase space formalism we construct the charges conjugate to supersymmetry, diffeomorphism and Lorentz transformations. The additional term in the action will lead to new, non-vanishing contributions to these charges. The magnetic diffeomorphism charges are equivalent to the ones previously found for gravity, while the dual supersymmetric charges are new and do not appear for the free Rarita-Schwinger field. The dual Lorentz charges serve to regularize the previous two. We find that the asymptotic symmetry group for supergravity can only include globally well-defined super-rotations.</jats:p

Phase space renormalization and finite BMS charges in six dimensions

Acknowledgements: We would like to thank Anupam A.H., Goncalo Araujo-Regado, Chandramouli Chowdhury, Adrien Fiorucci, Temple He, Daniel Kapec, Rifath Khan, Filipe S. Miguel, Enrico Parisini, Romain Ruzziconi, Kostas Skenderis, Marika Taylor and Zihan Yan for many useful conversations. F.C. kindly thanks DAMTP, Cambridge University for their hospitality. The research of F.C. is funded by the Deutsche Forschungsgemeinschaft (DFG) under Grant No. 406116891 within the Research Training Group RTG 2522/1, he also acknowledges support from the EPSRC Doctoral Prize Award EP/T517859/1 in the first part of this project. P.M. gratefully acknowledges support from the STFC consolidated grants ST/P000681/1 and ST/T000694/1 and thanks the STAG Research Center at the University of Southampton and TIFR, Mumbai for their hospitality. A.P. is supported by the National Research Foundation of Korea under the grants, NRF-2022R1A2B5B02002247, NRF-2020R1A2C1008497, he also acknowledges support from an Engineering and Physical Sciences Research Council (EPSRC) Mathematical Sciences Fellowship at the University of Southampton in the first part of this project. B.T. acknowledges support from the Cambridge Trust, King’s College, Cambridge and STFC consolidated grants ST/P000673/1 and ST/T00049X/1 and thanks the STAG Research Center at the University of Southampton for their hospitality.We perform a complete and systematic analysis of the solution space of six-dimensional Einstein gravity. We show that a particular subclass of solutions — those that are analytic near I+ — admit a non-trivial action of the generalised Bondi-Metzner-van der Burg-Sachs (GBMS) group which contains infinite-dimensional supertranslations and superrotations. The latter consists of all smooth volume-preserving Diff×Weyl transformations of the celestial S4. Using the covariant phase space formalism and a new technique which we develop in this paper (phase space renormalization), we are able to renormalize the symplectic potential using counterterms which are local and covariant. The Hamiltonian charges corresponding to GBMS diffeomorphisms are non-integrable. We show that the integrable part of these charges faithfully represent the GBMS algebra and in doing so, settle a long-standing open question regarding the existence of infinite-dimensional asymptotic symmetries in higher even dimensional non-linear gravity. Finally, we show that the semi-classical Ward identities for supertranslations and superrotations are precisely the leading and subleading soft-graviton theorems respectively

Phase space renormalization and finite BMS charges in six dimensions

Acknowledgements: We would like to thank Anupam A.H., Goncalo Araujo-Regado, Chandramouli Chowdhury, Adrien Fiorucci, Temple He, Daniel Kapec, Rifath Khan, Filipe S. Miguel, Enrico Parisini, Romain Ruzziconi, Kostas Skenderis, Marika Taylor and Zihan Yan for many useful conversations. F.C. kindly thanks DAMTP, Cambridge University for their hospitality. The research of F.C. is funded by the Deutsche Forschungsgemeinschaft (DFG) under Grant No. 406116891 within the Research Training Group RTG 2522/1, he also acknowledges support from the EPSRC Doctoral Prize Award EP/T517859/1 in the first part of this project. P.M. gratefully acknowledges support from the STFC consolidated grants ST/P000681/1 and ST/T000694/1 and thanks the STAG Research Center at the University of Southampton and TIFR, Mumbai for their hospitality. A.P. is supported by the National Research Foundation of Korea under the grants, NRF-2022R1A2B5B02002247, NRF-2020R1A2C1008497, he also acknowledges support from an Engineering and Physical Sciences Research Council (EPSRC) Mathematical Sciences Fellowship at the University of Southampton in the first part of this project. B.T. acknowledges support from the Cambridge Trust, King’s College, Cambridge and STFC consolidated grants ST/P000673/1 and ST/T00049X/1 and thanks the STAG Research Center at the University of Southampton for their hospitality.Abstract We perform a complete and systematic analysis of the solution space of six-dimensional Einstein gravity. We show that a particular subclass of solutions — those that are analytic near $$\mathcal{I}$$ I + — admit a non-trivial action of the generalised Bondi-Metzner-van der Burg-Sachs (GBMS) group which contains infinite-dimensional supertranslations and superrotations. The latter consists of all smooth volume-preserving Diff×Weyl transformations of the celestial S4. Using the covariant phase space formalism and a new technique which we develop in this paper (phase space renormalization), we are able to renormalize the symplectic potential using counterterms which are local and covariant. The Hamiltonian charges corresponding to GBMS diffeomorphisms are non-integrable. We show that the integrable part of these charges faithfully represent the GBMS algebra and in doing so, settle a long-standing open question regarding the existence of infinite-dimensional asymptotic symmetries in higher even dimensional non-linear gravity. Finally, we show that the semi-classical Ward identities for supertranslations and superrotations are precisely the leading and subleading soft-graviton theorems respectively.</jats:p