Correlation functions in N $$ \mathcal{N} $$ = 2 Supersymmetric vector matter Chern-Simons theory
Abstract Correlation functions of the higher-spin current operators in large N Chern-Simons theories are important to understand approximate higher-spin symmetries in these theories. Moreover, they also provide stronger checks for conjectured dualities in these theories. In this paper, we compute th...
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2020-04-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP04(2020)207 |
| _version_ | 1818112815982968832 |
|---|---|
| author | Karthik Inbasekar Sachin Jain Vinay Malvimat Abhishek Mehta Pranjal Nayak Tarun Sharma |
| author_facet | Karthik Inbasekar Sachin Jain Vinay Malvimat Abhishek Mehta Pranjal Nayak Tarun Sharma |
| author_sort | Karthik Inbasekar |
| collection | DOAJ |
| description | Abstract Correlation functions of the higher-spin current operators in large N Chern-Simons theories are important to understand approximate higher-spin symmetries in these theories. Moreover, they also provide stronger checks for conjectured dualities in these theories. In this paper, we compute the two, three and four-point functions of the operators in the spin zero multiplet of N $$ \mathcal{N} $$ = 2 Supersymmetric vector matter Chern-Simons theory at large N to all orders of ’t Hooft coupling. While the two- and three-point functions are computed by solving the Schwinger-Dyson equation, this method becomes intractable for the computation of the four-point functions. Thereby, we use bootstrap method to evaluate four-point function of scalar operator J 0 f = ψ ¯ ψ $$ {J}_0^f=\overline{\psi}\psi $$ and J 0 b = ϕ ¯ ϕ . $$ {J}_0^b=\overline{\phi}\phi . $$ Interestingly, because J 0 f J 0 f J 0 b $$ \left\langle {J}_0^f{J}_0^f{J}_0^b\right\rangle $$ is a contact term, the four point function of J 0 f $$ {J}_0^f $$ operator resembles the corresponding correlation function in the free theory, up to overall coupling constant dependent factors and up to some ‘bulk AdS’ contact terms. On the other hand the J 0 b $$ {J}_0^b $$ four-point function receives an additional contribution compared to the free theory expression due to the J 0 f $$ {J}_0^f $$ exchange. We find that the double discontinuity of this single trace operator J 0 f $$ {J}_0^f $$ vanishes and hence it only contributes to AdS-contact term. |
| first_indexed | 2024-12-11T03:24:56Z |
| format | Article |
| id | doaj.art-17a2c83cfba045a6866ffa4dcc5deacf |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-11T03:24:56Z |
| publishDate | 2020-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-17a2c83cfba045a6866ffa4dcc5deacf2022-12-22T01:22:32ZengSpringerOpenJournal of High Energy Physics1029-84792020-04-012020413610.1007/JHEP04(2020)207Correlation functions in N $$ \mathcal{N} $$ = 2 Supersymmetric vector matter Chern-Simons theoryKarthik Inbasekar0Sachin Jain1Vinay Malvimat2Abhishek Mehta3Pranjal Nayak4Tarun Sharma5Faculty of Exact Sciences, School of Physics and Astronomy, Tel Aviv UniversityIndian Institute of Science Education and ResearchIndian Institute of Science Education and ResearchIndian Institute of Science Education and ResearchDepartment of Physics & Astronomy, University of KentuckyDepartment of Physics, Brown UniversityAbstract Correlation functions of the higher-spin current operators in large N Chern-Simons theories are important to understand approximate higher-spin symmetries in these theories. Moreover, they also provide stronger checks for conjectured dualities in these theories. In this paper, we compute the two, three and four-point functions of the operators in the spin zero multiplet of N $$ \mathcal{N} $$ = 2 Supersymmetric vector matter Chern-Simons theory at large N to all orders of ’t Hooft coupling. While the two- and three-point functions are computed by solving the Schwinger-Dyson equation, this method becomes intractable for the computation of the four-point functions. Thereby, we use bootstrap method to evaluate four-point function of scalar operator J 0 f = ψ ¯ ψ $$ {J}_0^f=\overline{\psi}\psi $$ and J 0 b = ϕ ¯ ϕ . $$ {J}_0^b=\overline{\phi}\phi . $$ Interestingly, because J 0 f J 0 f J 0 b $$ \left\langle {J}_0^f{J}_0^f{J}_0^b\right\rangle $$ is a contact term, the four point function of J 0 f $$ {J}_0^f $$ operator resembles the corresponding correlation function in the free theory, up to overall coupling constant dependent factors and up to some ‘bulk AdS’ contact terms. On the other hand the J 0 b $$ {J}_0^b $$ four-point function receives an additional contribution compared to the free theory expression due to the J 0 f $$ {J}_0^f $$ exchange. We find that the double discontinuity of this single trace operator J 0 f $$ {J}_0^f $$ vanishes and hence it only contributes to AdS-contact term.http://link.springer.com/article/10.1007/JHEP04(2020)2071/N ExpansionChern-Simons TheoriesHigher Spin SymmetryField Theories in Lower Dimensions |
| spellingShingle | Karthik Inbasekar Sachin Jain Vinay Malvimat Abhishek Mehta Pranjal Nayak Tarun Sharma Correlation functions in N $$ \mathcal{N} $$ = 2 Supersymmetric vector matter Chern-Simons theory Journal of High Energy Physics 1/N Expansion Chern-Simons Theories Higher Spin Symmetry Field Theories in Lower Dimensions |
| title | Correlation functions in N $$ \mathcal{N} $$ = 2 Supersymmetric vector matter Chern-Simons theory |
| title_full | Correlation functions in N $$ \mathcal{N} $$ = 2 Supersymmetric vector matter Chern-Simons theory |
| title_fullStr | Correlation functions in N $$ \mathcal{N} $$ = 2 Supersymmetric vector matter Chern-Simons theory |
| title_full_unstemmed | Correlation functions in N $$ \mathcal{N} $$ = 2 Supersymmetric vector matter Chern-Simons theory |
| title_short | Correlation functions in N $$ \mathcal{N} $$ = 2 Supersymmetric vector matter Chern-Simons theory |
| title_sort | correlation functions in n mathcal n 2 supersymmetric vector matter chern simons theory |
| topic | 1/N Expansion Chern-Simons Theories Higher Spin Symmetry Field Theories in Lower Dimensions |
| url | http://link.springer.com/article/10.1007/JHEP04(2020)207 |
| work_keys_str_mv | AT karthikinbasekar correlationfunctionsinnmathcaln2supersymmetricvectormatterchernsimonstheory AT sachinjain correlationfunctionsinnmathcaln2supersymmetricvectormatterchernsimonstheory AT vinaymalvimat correlationfunctionsinnmathcaln2supersymmetricvectormatterchernsimonstheory AT abhishekmehta correlationfunctionsinnmathcaln2supersymmetricvectormatterchernsimonstheory AT pranjalnayak correlationfunctionsinnmathcaln2supersymmetricvectormatterchernsimonstheory AT tarunsharma correlationfunctionsinnmathcaln2supersymmetricvectormatterchernsimonstheory |