Melonic theories over diverse number systems
Melonic field theories are defined over the p-adic numbers with the help of a sign character. Our construction works over the reals as well as the p-adics, and it includes the fermionic and bosonic Klebanov-Tarnopolsky models as special cases; depending on the sign character, the symmetry group of t...
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| Main Authors: | , , , , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
13 December 2018
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| In: |
Physical review
Year: 2018, Volume: 98, Issue: 12 |
| ISSN: | 2470-0029 |
| DOI: | 10.1103/PhysRevD.98.126007 |
| Online Access: | Resolving-System, Volltext: http://dx.doi.org/10.1103/PhysRevD.98.126007 Verlag, Volltext: https://link.aps.org/doi/10.1103/PhysRevD.98.126007 
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| Author Notes: | Steven S. Gubser, Matthew Heydeman, Christian Jepsen, Sarthak Parikh, Ingmar Saberi, Bogdan Stoica, and Brian Trundy |
| Summary: | Melonic field theories are defined over the p-adic numbers with the help of a sign character. Our construction works over the reals as well as the p-adics, and it includes the fermionic and bosonic Klebanov-Tarnopolsky models as special cases; depending on the sign character, the symmetry group of the field theory can be either orthogonal or symplectic. Analysis of the Schwinger-Dyson equation for the two-point function in the leading melonic limit shows that power law scaling behavior in the infrared arises for fermionic theories when the sign character is non-trivial, and for bosonic theories when the sign character is trivial. In certain cases, the Schwinger-Dyson equation can be solved exactly using a quartic polynomial equation, and the solution interpolates between the ultraviolet scaling controlled by the spectral parameter and the universal infrared scaling. As a by-product of our analysis, we see that melonic field theories defined over the real numbers can be modified by replacing the time derivative by a bilocal kinetic term with a continuously variable spectral parameter. The infrared scaling of the resulting two-point function is universal, independent of the spectral parameter of the ultraviolet theory. |
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| Item Description: | Gesehen am 27.02.2019 |
| Physical Description: | Online Resource |
| ISSN: | 2470-0029 |
| DOI: | 10.1103/PhysRevD.98.126007 |