Massless Lifshitz Field Theory for Arbitrary $z$
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910528035618816 |
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| author | Basak, Jaydeep Kumar Chakraborty, Adrita Chu, Chong-Sun Giataganas, Dimitrios Parihar, Himanshu |
| author_facet | Basak, Jaydeep Kumar Chakraborty, Adrita Chu, Chong-Sun Giataganas, Dimitrios Parihar, Himanshu |
| contents | By using the notion of fractional derivatives, we introduce a class of massless Lifshitz scalar field theory in (1+1)-dimension with an arbitrary anisotropy index $z$. The Lifshitz scale invariant ground state of the theory is constructed explicitly and takes the form of Rokhsar-Kivelson (RK). We show that there is a continuous family of ground states with degeneracy parameterized by the choice of solution to the equation of motion of an auxiliary classical system. The quantum mechanical path integral establishes a 2d/1d correspondence with the equal time correlation functions of the Lifshitz scalar field theory. We study the entanglement properties of the Lifshitz theory for arbitrary $z$ using the path integral representation. The entanglement measures are expressed in terms of certain cross ratio functions we specify, and satisfy the $c$-function monotonicity theorems. We also consider the holographic description of the Lifshitz theory. In order to match with the field theory result for the entanglement entropy, we propose a $z$-dependent radius scale for the Lifshitz background. This relation is consistent with the $z$-dependent scaling symmetry respected by the Lifshitz vacuum. Furthermore, the time-like entanglement entropy is determined using holography. Our result suggests that there should exist a fundamental definition of time-like entanglement other than employing analytic continuation as performed in relativistic field theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_16284 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Massless Lifshitz Field Theory for Arbitrary $z$ Basak, Jaydeep Kumar Chakraborty, Adrita Chu, Chong-Sun Giataganas, Dimitrios Parihar, Himanshu High Energy Physics - Theory Strongly Correlated Electrons By using the notion of fractional derivatives, we introduce a class of massless Lifshitz scalar field theory in (1+1)-dimension with an arbitrary anisotropy index $z$. The Lifshitz scale invariant ground state of the theory is constructed explicitly and takes the form of Rokhsar-Kivelson (RK). We show that there is a continuous family of ground states with degeneracy parameterized by the choice of solution to the equation of motion of an auxiliary classical system. The quantum mechanical path integral establishes a 2d/1d correspondence with the equal time correlation functions of the Lifshitz scalar field theory. We study the entanglement properties of the Lifshitz theory for arbitrary $z$ using the path integral representation. The entanglement measures are expressed in terms of certain cross ratio functions we specify, and satisfy the $c$-function monotonicity theorems. We also consider the holographic description of the Lifshitz theory. In order to match with the field theory result for the entanglement entropy, we propose a $z$-dependent radius scale for the Lifshitz background. This relation is consistent with the $z$-dependent scaling symmetry respected by the Lifshitz vacuum. Furthermore, the time-like entanglement entropy is determined using holography. Our result suggests that there should exist a fundamental definition of time-like entanglement other than employing analytic continuation as performed in relativistic field theory. |
| title | Massless Lifshitz Field Theory for Arbitrary $z$ |
| topic | High Energy Physics - Theory Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2312.16284 |