A worldline theory for supergravity
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Springer
Received: May 24, 2020 Accepted: June 1, 2020 Published: June 16, 2020
A worldline theory for supergravity
a
Institute for Physics, Humboldt University Berlin, Zum Großen Windkanal 6, D-12489 Berlin, Germany b Department of Natural Sciences, The Open University of Israel, PO Box 808, Ra’anana 43537, Israel c Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilian-Universit¨ at, Theresienstr. 37, D-80333 M¨ unchen, Germany
E-mail: [email protected], [email protected], [email protected] Abstract: The N = 4 supersymmetric spinning particle admits several consistent quantizations, related to the gauging of different subgroups of the SO(4) R-symmetry on the worldline. We construct the background independent BRST quantization for all of these choices which are shown to reproduce either the massless NS-NS spectrum of the string, or Einstein theory with or without the antisymmetric tensor field and/or dilaton corresponding to different restrictions. Quantum consistency of the worldline implies equations of motion for the background which, in addition to the admissible string backgrounds, admit Einstein manifolds with or whithout a cosmological constant. The vertex operators for the Kalb-Ramond, graviton and dilaton fields are obtained from the linear variations of the BRST charge. They produce the physical states by action on the diffeomorphism ghost states. Keywords: BRST Quantization, Gauge Symmetry ArXiv ePrint: 2004.06129 In honor of Samson Shatashvili’s 60th birthday
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP06(2020)103
JHEP06(2020)103
Roberto Bonezzi,a Adiel Meyerb and Ivo Sachsc
Contents 1
2 N = 4 spinning particle and NS-NS spectrum 2.1 Gauging the R-symmetries 2.2 Dirac quantization
3 5 6
3 BRST quantization 3.1 Reducing the BRST cohomology 3.2 Reduced BV-spectrum
6 7 9
4 N = 4 point particle coupled to background fields 4.1 Pure gravity 4.2 Coupling the B-field 4.2.1 Vertex operator for the B-field 4.3 Coupling to the dilaton 4.3.1 Dilaton vertex operator 4.4 Fully coupled system
11 11 12 15 16 19 20
5 Conclusions
22
A Alternative dilaton coupling
23
1
Introduction and summary of results
The fact that critical string theory contains a massless graviton in its spectrum and that the consistency of the worldsheet conformal field theory implies the vacuum Einstein equations are generally considered important consistency tests for string theory to be a theory of quantum gravity. On the other hand, in string theory the graviton always comes together with the dilaton and, depending on the model, also an anti-symmetric Kalb-Ramond tensor field. Another important feature in string theory is the operator state correspondence which asserts that any scattering state can be represented by insertion of a suitable vertex operator on the worldsheet. Finally, the absence of conformal anomalies implies coupled equations for all of these fields. These equations are rather restrictive. In particular, they do not see
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