Opus on conformal symmetry of the Nambu-Goto versus Polyakov strings

Article Physics, Particles & Fields

Notes on higher-derivative conformal theory with nonprimary energy-momentum tensor that applies to the Nambu-Goto string

Yuri Makeenko

Summary: I investigate the higher-derivative conformal theory and distinguish the Nambu-Goto and Polyakov strings. The energy-momentum tensor is conserved and traceless but not of the unit operator's conformal family. To achieve conformal invariance in this case, I develop a new technique that explicitly considers the quantum equation of motion, leading to singular products. I demonstrate that the conformal transformations generated by the nonprimary energy-momentum tensor form a Lie algebra with a central extension, contributing to a logarithmically divergent central charge in the path-integral formalism. I show how the logarithmic divergence is canceled in the string susceptibility and reproduce the previously obtained deviation from KPZ-DDK at one loop.

JOURNAL OF HIGH ENERGY PHYSICS (2023)

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Article Astronomy & Astrophysics

The susceptibility exponent of Nambu-Goto strings

Jan Ambjorn et al.

Summary: The string susceptibility gamma(str) for the regularized Nambu-Goto string in various dimensions was computed, and it was found that gamma(str) = 1/2 in the range 2 < d < 26, consistent with previous results obtained for lattice strings.

MODERN PHYSICS LETTERS A (2021)

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Article Physics, Particles & Fields

Private life of the Liouville field that causes new anomalies in the Nambu-Goto string

Yuri Makeenko

Summary: In this study, I investigated the higher-order terms of the Seeley expansion of the heat kernel and their impact on the string effective action, demonstrating anomalous contributions for the Polyakov string consistent with the KPZ-DDK result for the Liouville theory. However, a deviation was found for the Nambu-Goto string formulation, suggesting potential differences between the two string descriptions.

NUCLEAR PHYSICS B (2021)

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Article Astronomy & Astrophysics