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Towards Lefschetz Thimbles in Sigma Models, I
We study two dimensional path integral Lefschetz thimbles, i.e. the possible path integration contours. Specifically, in the examples of the O ( N ) and models, we find a large class of complex critical points of the sigma model actions which are relevant for the theory in finite volume at finite te...
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| Published in: | Journal of experimental and theoretical physics 2021-04, Vol.132 (4), p.734-751 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| container_end_page | 751 |
| container_issue | 4 |
| container_start_page | 734 |
| container_title | Journal of experimental and theoretical physics |
| container_volume | 132 |
| creator | Krichever, I. Nekrasov, N. |
| description | We study two dimensional path integral Lefschetz thimbles, i.e. the possible path integration contours. Specifically, in the examples of the
O
(
N
) and
models, we find a large class of complex critical points of the sigma model actions which are relevant for the theory in finite volume at finite temperature, with various chemical potentials corresponding to the symmetries of the models. In this paper we discuss the case of the
O
(2
m
) and the
models in the sector of zero instanton charge, as well as some solutions of the
O
(2
m
+ 1) model. The
-model for all instanton charges and a more general class of solutions of the
O
(
N
)-model with odd
N
will be discussed in the forthcoming paper. |
| doi_str_mv | 10.1134/S1063776121040129 |
| format | article |
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O
(
N
) and
models, we find a large class of complex critical points of the sigma model actions which are relevant for the theory in finite volume at finite temperature, with various chemical potentials corresponding to the symmetries of the models. In this paper we discuss the case of the
O
(2
m
) and the
models in the sector of zero instanton charge, as well as some solutions of the
O
(2
m
+ 1) model. The
-model for all instanton charges and a more general class of solutions of the
O
(
N
)-model with odd
N
will be discussed in the forthcoming paper.</description><identifier>ISSN: 1063-7761</identifier><identifier>EISSN: 1090-6509</identifier><identifier>DOI: 10.1134/S1063776121040129</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Classical and Quantum Gravitation ; Critical point ; Elementary Particles ; Instantons ; Particle and Nuclear Physics ; Physics ; Physics and Astronomy ; Quantum Field Theory ; Relativity Theory ; Solid State Physics ; Two dimensional models</subject><ispartof>Journal of experimental and theoretical physics, 2021-04, Vol.132 (4), p.734-751</ispartof><rights>Pleiades Publishing, Inc. 2021. ISSN 1063-7761, Journal of Experimental and Theoretical Physics, 2021, Vol. 132, No. 4, pp. 734–751. © Pleiades Publishing, Inc., 2021. Russian Text © The Author(s), 2021, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2021, Vol. 159, No. 4, pp. 822–848.</rights><rights>COPYRIGHT 2021 Springer</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c389t-ade0319b4b619652b2e41086cdea77b9cd9d902ea55302f8cd3a84a9a58aeaba3</citedby><cites>FETCH-LOGICAL-c389t-ade0319b4b619652b2e41086cdea77b9cd9d902ea55302f8cd3a84a9a58aeaba3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Krichever, I.</creatorcontrib><creatorcontrib>Nekrasov, N.</creatorcontrib><title>Towards Lefschetz Thimbles in Sigma Models, I</title><title>Journal of experimental and theoretical physics</title><addtitle>J. Exp. Theor. Phys</addtitle><description>We study two dimensional path integral Lefschetz thimbles, i.e. the possible path integration contours. Specifically, in the examples of the
O
(
N
) and
models, we find a large class of complex critical points of the sigma model actions which are relevant for the theory in finite volume at finite temperature, with various chemical potentials corresponding to the symmetries of the models. In this paper we discuss the case of the
O
(2
m
) and the
models in the sector of zero instanton charge, as well as some solutions of the
O
(2
m
+ 1) model. The
-model for all instanton charges and a more general class of solutions of the
O
(
N
)-model with odd
N
will be discussed in the forthcoming paper.</description><subject>Classical and Quantum Gravitation</subject><subject>Critical point</subject><subject>Elementary Particles</subject><subject>Instantons</subject><subject>Particle and Nuclear Physics</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Field Theory</subject><subject>Relativity Theory</subject><subject>Solid State Physics</subject><subject>Two dimensional models</subject><issn>1063-7761</issn><issn>1090-6509</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp1kF1LwzAUhoMoOKc_wLuCV4KdJ0mbNpdj-DGYCG5eh7Q57Tr6MZMOP369GRVkiOTihJznOW84hFxSmFDKo9slBcGTRFBGIQLK5BEZUZAQihjk8f4ueLjvn5Iz5zYAkDKQIxKuundtjQsWWLh8jf1XsFpXTVajC6o2WFZlo4OnzmDtboL5OTkpdO3w4qeOyev93Wr2GC6eH-az6SLMeSr7UBsETmUWZYJKEbOMYUQhFblBnSSZzI00EhjqOObAijQ3XKeRljpONepM8zG5GuZubfe2Q9erTbezrY9ULOaRYFywyFOTgSp1japqi663OvfHYFPlXYtF5d-nQgjm01jihesDwTM9fvSl3jmn5suXQ5YObG475ywWamurRttPRUHtV67-rNw7bHCcZ9sS7e-3_5e-AQOjfz8</recordid><startdate>20210401</startdate><enddate>20210401</enddate><creator>Krichever, I.</creator><creator>Nekrasov, N.</creator><general>Pleiades Publishing</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>ISR</scope></search><sort><creationdate>20210401</creationdate><title>Towards Lefschetz Thimbles in Sigma Models, I</title><author>Krichever, I. ; Nekrasov, N.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c389t-ade0319b4b619652b2e41086cdea77b9cd9d902ea55302f8cd3a84a9a58aeaba3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Classical and Quantum Gravitation</topic><topic>Critical point</topic><topic>Elementary Particles</topic><topic>Instantons</topic><topic>Particle and Nuclear Physics</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Field Theory</topic><topic>Relativity Theory</topic><topic>Solid State Physics</topic><topic>Two dimensional models</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Krichever, I.</creatorcontrib><creatorcontrib>Nekrasov, N.</creatorcontrib><collection>CrossRef</collection><collection>Gale in Context: Science</collection><jtitle>Journal of experimental and theoretical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Krichever, I.</au><au>Nekrasov, N.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Towards Lefschetz Thimbles in Sigma Models, I</atitle><jtitle>Journal of experimental and theoretical physics</jtitle><stitle>J. Exp. Theor. Phys</stitle><date>2021-04-01</date><risdate>2021</risdate><volume>132</volume><issue>4</issue><spage>734</spage><epage>751</epage><pages>734-751</pages><issn>1063-7761</issn><eissn>1090-6509</eissn><abstract>We study two dimensional path integral Lefschetz thimbles, i.e. the possible path integration contours. Specifically, in the examples of the
O
(
N
) and
models, we find a large class of complex critical points of the sigma model actions which are relevant for the theory in finite volume at finite temperature, with various chemical potentials corresponding to the symmetries of the models. In this paper we discuss the case of the
O
(2
m
) and the
models in the sector of zero instanton charge, as well as some solutions of the
O
(2
m
+ 1) model. The
-model for all instanton charges and a more general class of solutions of the
O
(
N
)-model with odd
N
will be discussed in the forthcoming paper.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S1063776121040129</doi><tpages>18</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1063-7761 |
| ispartof | Journal of experimental and theoretical physics, 2021-04, Vol.132 (4), p.734-751 |
| issn | 1063-7761 1090-6509 |
| language | eng |
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| source | Springer Link |
| subjects | Classical and Quantum Gravitation Critical point Elementary Particles Instantons Particle and Nuclear Physics Physics Physics and Astronomy Quantum Field Theory Relativity Theory Solid State Physics Two dimensional models |
| title | Towards Lefschetz Thimbles in Sigma Models, I |
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