Path integral for the closed superstring and the matrix model
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866909013011070976 |
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| author | Asano, Yuhma |
| author_facet | Asano, Yuhma |
| contents | The IKKT matrix model, which is proposed as a non-perturbative formulation of superstring theory, has an issue typical of zero-dimensional theory -- ambiguity in the definition of its path integral. To tackle this issue, we revisit the path-integral formulation of perturbative string theory. In this article, we review recent progress in the string world-sheet path-integral formulation, especially in the Minkowski signature. We first derive the Minkowskian path integral of the Nambu-Goto type equivalent to Polyakov's Euclidean path integral for critical closed string theory, showing equivalences among the Nambu-Goto-, Schild- and Polyakov-type formulations both in the Minkowskian and Euclidean signatures. We also show that ``stringy causality'' is realised in the path-integral formulation at the level of string perturbation theory. We then obtain the matrix model with a property like the stringy causality, which turns out to be a Minkowskian version of the NBI-type IKKT matrix model, by matrix regularisation of the path integral for perturbative type IIB string theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_25052 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Path integral for the closed superstring and the matrix model Asano, Yuhma High Energy Physics - Theory The IKKT matrix model, which is proposed as a non-perturbative formulation of superstring theory, has an issue typical of zero-dimensional theory -- ambiguity in the definition of its path integral. To tackle this issue, we revisit the path-integral formulation of perturbative string theory. In this article, we review recent progress in the string world-sheet path-integral formulation, especially in the Minkowski signature. We first derive the Minkowskian path integral of the Nambu-Goto type equivalent to Polyakov's Euclidean path integral for critical closed string theory, showing equivalences among the Nambu-Goto-, Schild- and Polyakov-type formulations both in the Minkowskian and Euclidean signatures. We also show that ``stringy causality'' is realised in the path-integral formulation at the level of string perturbation theory. We then obtain the matrix model with a property like the stringy causality, which turns out to be a Minkowskian version of the NBI-type IKKT matrix model, by matrix regularisation of the path integral for perturbative type IIB string theory. |
| title | Path integral for the closed superstring and the matrix model |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.25052 |