Strongly Coupled 𝒫𝒯-Symmetric Models in Holography
Non-Hermitian quantum field theories are a promising tool to study open quantum systems. These theories preserve unitarity if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">PT...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-12-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/27/1/13 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832588586785964032 |
|---|---|
| author | Daniel Areán David Garcia-Fariña Karl Landsteiner |
| author_facet | Daniel Areán David Garcia-Fariña Karl Landsteiner |
| author_sort | Daniel Areán |
| collection | DOAJ |
| description | Non-Hermitian quantum field theories are a promising tool to study open quantum systems. These theories preserve unitarity if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">PT</mi></semantics></math></inline-formula> symmetry is respected, and in that case, an equivalent Hermitian description exists via the so-called Dyson map. Generically, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">PT</mi></semantics></math></inline-formula>-symmetric non-Hermitian theories can also feature phases where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">PT</mi></semantics></math></inline-formula> symmetry is broken and unitarity is lost. We review the construction of holographic duals to strongly coupled <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">PT</mi></semantics></math></inline-formula>-symmetric quantum field theories and the study of their phase diagram. We next focus on spacetime-dependent non-Hermitian couplings: non-Hermitian quenches and lattices. They violate the null energy condition in the gravity dual. The lattices realize phases supporting an imaginary current that breaks <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">PT</mi></semantics></math></inline-formula> symmetry spontaneously. Remarkably, these non-Hermitian lattices flow to a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">PT</mi></semantics></math></inline-formula>-symmetric fixed point in the IR. |
| format | Article |
| id | doaj-art-e31983dff425499285bfe6b33567320f |
| institution | Kabale University |
| issn | 1099-4300 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-e31983dff425499285bfe6b33567320f2025-01-24T13:31:39ZengMDPI AGEntropy1099-43002024-12-012711310.3390/e27010013Strongly Coupled 𝒫𝒯-Symmetric Models in HolographyDaniel Areán0David Garcia-Fariña1Karl Landsteiner2Instituto de Física Teórica UAM/CSIC, Campus de Cantoblanco, c/Nicolás Cabrera 13-15, 28049 Madrid, SpainInstituto de Física Teórica UAM/CSIC, Campus de Cantoblanco, c/Nicolás Cabrera 13-15, 28049 Madrid, SpainInstituto de Física Teórica UAM/CSIC, Campus de Cantoblanco, c/Nicolás Cabrera 13-15, 28049 Madrid, SpainNon-Hermitian quantum field theories are a promising tool to study open quantum systems. These theories preserve unitarity if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">PT</mi></semantics></math></inline-formula> symmetry is respected, and in that case, an equivalent Hermitian description exists via the so-called Dyson map. Generically, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">PT</mi></semantics></math></inline-formula>-symmetric non-Hermitian theories can also feature phases where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">PT</mi></semantics></math></inline-formula> symmetry is broken and unitarity is lost. We review the construction of holographic duals to strongly coupled <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">PT</mi></semantics></math></inline-formula>-symmetric quantum field theories and the study of their phase diagram. We next focus on spacetime-dependent non-Hermitian couplings: non-Hermitian quenches and lattices. They violate the null energy condition in the gravity dual. The lattices realize phases supporting an imaginary current that breaks <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">PT</mi></semantics></math></inline-formula> symmetry spontaneously. Remarkably, these non-Hermitian lattices flow to a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">PT</mi></semantics></math></inline-formula>-symmetric fixed point in the IR.https://www.mdpi.com/1099-4300/27/1/13non-Hermitian physicsPT symmetrygauge/gravity duality |
| spellingShingle | Daniel Areán David Garcia-Fariña Karl Landsteiner Strongly Coupled 𝒫𝒯-Symmetric Models in Holography Entropy non-Hermitian physics PT symmetry gauge/gravity duality |
| title | Strongly Coupled 𝒫𝒯-Symmetric Models in Holography |
| title_full | Strongly Coupled 𝒫𝒯-Symmetric Models in Holography |
| title_fullStr | Strongly Coupled 𝒫𝒯-Symmetric Models in Holography |
| title_full_unstemmed | Strongly Coupled 𝒫𝒯-Symmetric Models in Holography |
| title_short | Strongly Coupled 𝒫𝒯-Symmetric Models in Holography |
| title_sort | strongly coupled 𝒫𝒯 symmetric models in holography |
| topic | non-Hermitian physics PT symmetry gauge/gravity duality |
| url | https://www.mdpi.com/1099-4300/27/1/13 |
| work_keys_str_mv | AT danielarean stronglycoupledptsymmetricmodelsinholography AT davidgarciafarina stronglycoupledptsymmetricmodelsinholography AT karllandsteiner stronglycoupledptsymmetricmodelsinholography |