### Abstract

We study the unitary representations of the non-compact real forms of the complex Lie superalgebra sl(n | m). Among them, only the real form su(p , q | m) with (p + q = n) admits nontrivial unitary representations, and all such representations are of the highest-weight type (or the lowest-weight type). We extend the standard oscillator construction of the unitary representations of non-compact Lie superalgebras over standard Fock spaces to generalised Fock spaces which allows us to define the action of oscillator determinants raised to non-integer powers. We prove that the proposed construction yields all the unitary representations including those with continuous labels. The unitary representations can be diagrammatically represented by non-compact Young diagrams. We apply our general results to the physically important case of four-dimensional conformal superalgebra su(2 , 2 | 4) and show how it yields readily its unitary representations including those corresponding to supermultiplets of conformal fields with continuous (anomalous) scaling dimensions.[Figure not available: see fulltext.]

Original language | English (US) |
---|---|

Journal | Communications In Mathematical Physics |

DOIs | |

State | Published - Jan 1 2019 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

}

**The Complete Unitary Dual of Non-compact Lie Superalgebra su(p , q | m) via the Generalised Oscillator Formalism, and Non-compact Young Diagrams.** / Gunaydin, Murat; Volin, Dmytro.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The Complete Unitary Dual of Non-compact Lie Superalgebra su(p , q | m) via the Generalised Oscillator Formalism, and Non-compact Young Diagrams

AU - Gunaydin, Murat

AU - Volin, Dmytro

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We study the unitary representations of the non-compact real forms of the complex Lie superalgebra sl(n | m). Among them, only the real form su(p , q | m) with (p + q = n) admits nontrivial unitary representations, and all such representations are of the highest-weight type (or the lowest-weight type). We extend the standard oscillator construction of the unitary representations of non-compact Lie superalgebras over standard Fock spaces to generalised Fock spaces which allows us to define the action of oscillator determinants raised to non-integer powers. We prove that the proposed construction yields all the unitary representations including those with continuous labels. The unitary representations can be diagrammatically represented by non-compact Young diagrams. We apply our general results to the physically important case of four-dimensional conformal superalgebra su(2 , 2 | 4) and show how it yields readily its unitary representations including those corresponding to supermultiplets of conformal fields with continuous (anomalous) scaling dimensions.[Figure not available: see fulltext.]

AB - We study the unitary representations of the non-compact real forms of the complex Lie superalgebra sl(n | m). Among them, only the real form su(p , q | m) with (p + q = n) admits nontrivial unitary representations, and all such representations are of the highest-weight type (or the lowest-weight type). We extend the standard oscillator construction of the unitary representations of non-compact Lie superalgebras over standard Fock spaces to generalised Fock spaces which allows us to define the action of oscillator determinants raised to non-integer powers. We prove that the proposed construction yields all the unitary representations including those with continuous labels. The unitary representations can be diagrammatically represented by non-compact Young diagrams. We apply our general results to the physically important case of four-dimensional conformal superalgebra su(2 , 2 | 4) and show how it yields readily its unitary representations including those corresponding to supermultiplets of conformal fields with continuous (anomalous) scaling dimensions.[Figure not available: see fulltext.]

UR - http://www.scopus.com/inward/record.url?scp=85064340742&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85064340742&partnerID=8YFLogxK

U2 - 10.1007/s00220-019-03406-7

DO - 10.1007/s00220-019-03406-7

M3 - Article

AN - SCOPUS:85064340742

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

ER -