On the equilibrium measure for the Lukyanov integral
| Autor: | Guera, Charlie Dworaczek, Kozlowski, Karol K. |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In 2000, Lukyanov conjectured that a certain ratio of $N$-fold integrals should provide access, in the large-$N$ regime, to the ground state expectation value of the exponential of the Sinh-Gordon quantum field in 1+1 dimensions and finite volume $R$. This work aims at rigorously constructing the fundamental objects necessary to address the large-$N$ analysis of such integrals. More precisely, we construct and establish the main properties of the the equilibrium measure minimising a certain $N$-dependent energy functional that naturally arises in the study of the leading large-$N$ behaviour of the Lukyanov integral. Our construction allows us to heuristically advocate the leading term in the large-$N$ asymptotic behaviour of the mentioned ratio of Lukyanov integrals, hence supporting Lukyanov's prediction -- obtained by other means -- on the exponent $\sigma$ of the power-law $N^{\sigma}$ term of its asymptotic expansion as $N\rightarrow + \infty$. Comment: 32 pages, 1 figures |
| Databáze: | arXiv |
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