Origin of higher Schwarzians - INSPIRE

DataBETA

Origin of higher Schwarzians

Sergey Krivonos
(
- Tomsk State U.
)

Jan 19, 2024

8 pages

Published in:

Phys.Rev.D 109 (2024) 6, 065029

Published: Mar 15, 2024

e-Print:

2401.10532 [hep-th]

DOI:

10.1103/PhysRevD.109.065029 (publication)

View in:

ADS Abstract Service

reference search2 citations

Citations per year

Abstract: (APS)

In this paper we analyze higher Schwarzians and show that they are closely related to the nonlinear realization of the Virasoro algebra. The Goldstone fields of such a realization provide a new set of

S L (2, R)

invariant higher Schwarzians that are deeply related to those of Aharonov [Duke Math. J. 36, 599 (1969)], Tamanoi [Math. Ann. 305, 127 (1996)], and Bonora-Matone [Nucl. Phys. B327, 415 (1989); Int. J. Mod. Phys. A 10, 289 (1995); ]. A minor change of the coset space parametrization leads to a new set of

S L (2, R)

noninvariant higher Schwarzians now related to the Schippers [Proc. Am. Math. Soc. 128, 3241 (2000)] and Bertilsson [Ark. Mat. 36, 255 (1998)] Schwarzians.

Note:

8 pages; minor corrections, accepted in Phys Rev D

representation: nonlinear
algebra: Virasoro
invariance: SL(2,R)
coset space
parametrization

References(19)

Figures(0)

[1]

What is the Schwarzian derivative?

V. Ovsienko
,
S. Tabachnikov

- Not.Amer.Math.Soc. 56 (2009) 34

[2]

A necessary and sufficient condition for univalence of a meromorphic function

D. Aharonov

- Duke Math.J. 36 (1969) 599

[3]

Higher Schwarzian operators and combinatorics of the Schwarzian derivatives

H. Tamanoi

- Math.Ann. 305 (1996) 127

[4]

Distortion theorems for higher order Schwarzian derivatives of univalent functions

E. Schippers

- Proc.Am.Math.Soc. 128 (2000) 3241

[5]

Coefficient estimates for negative powers of the derivative of univalent functions

D. Bertilsson

- Ark.Mat. 36 (1998) 255

[6]

The Schwarzian derivative and Schlicht functions

Z. Nehari

- Bull.Am.Math.Soc. 55 (1949) 545

[7]

Invariant Schwarzian derivatives of higher order, Complex Anal. Oper. Theor. 5, 659

S.-A Kim
,
T. Sugawa

[8]

The inverse Higgs phenomenon in nonlinear realizations

E.A. Ivanov
,
V.I. Ogievetsky

- Theor.Math.Phys. 25 (1975) 1050

[9]

Schwarzian mechanics via nonlinear realizations

Anton Galajinsky
(
- Tomsk Polytechnic U.
)

- Phys.Lett.B 795 (2019) 277-280
•
e-Print:
- 1905.01935
•
DOI:
- 10.1016/j.physletb.2019.05.054

[10]

Super-Schwarzians via nonlinear realizations

Anton Galajinsky
(
- TUSUR, Tomsk
)

- JHEP 06 (2020) 027
•
e-Print:
- 2004.04489
•
DOI:
- 10.1007/JHEP06(2020)027

[11]

$\mathcal{N=3}$ super–Schwarzian from $OSp (3|2)$ invariants

Anton Galajinsky
(
- Tomsk Polytechnic U.
)

- Phys.Lett.B 811 (2020) 135885
•
e-Print:
- 2009.13064
•
DOI:
- 10.1016/j.physletb.2020.135885

[12]

$\mathcal {N}$ =4 super-Schwarzian derivative via nonlinear realizations

Anton Galajinsky
(
- TUSUR, Tomsk
)
,
Sergey Krivonos
(
- Dubna, JINR
)

- Phys.Rev.D 102 (2020) 10, 106015
•
e-Print:
- 2007.04015
•
DOI:
- 10.1103/PhysRevD.102.106015

[13]

Generalized Schwarzians

Nikolay Kozyrev
(
- Dubna, JINR
)
,
Sergey Krivonos
(
- Dubna, JINR
)

- Phys.Rev.D 107 (2023) 2, 026018
•
e-Print:
- 2211.14021
•
DOI:
- 10.1103/PhysRevD.107.026018

[14]

(Super)Schwarzian mechanics

Nikolay Kozyrev
(
- Dubna, JINR
)
,
Sergey Krivonos
(
- Dubna, JINR
)

- JHEP 03 (2022) 120
•
e-Print:
- 2111.04643
•
DOI:
- 10.1007/JHEP03(2022)120

[15]

N ¼ 4 supersymmetric Schwarzian with Dð1

N. Kozyrev
,
S. Krivonos

[15]

$\mathcal{N}$ =4 supersymmetric Schwarzian with $D(1,2;\alpha)$ symmetry

Nikolay Kozyrev
(
- Dubna, JINR
)
,
Sergey Krivonos
(
- Dubna, JINR
)

- Phys.Rev.D 105 (2022) 8, 085010
•
e-Print:
- 2112.14481
•
DOI:
- 10.1103/PhysRevD.105.085010

[16]

KdV EQUATION ON RIEMANN SURFACES

L. Bonora
(
- Sissa, Trieste and
- INFN, Trieste
)
,
Marco Matone
(
- Sissa, Trieste and
- INFN, Trieste
)

- Nucl.Phys.B 327 (1989) 415-426
•
DOI:
- 10.1016/0550-3213(89)90277-0

[16]

Uniformization theory and 2-D gravity. 1. Liouville action and intersection numbers

Marco Matone
(
- Imperial Coll., London and
- Padua U. and
- INFN, Padua
)

- Int.J.Mod.Phys.A 10 (1995) 289-336
•
e-Print:
- hep-th/9306150
•
DOI:
- 10.1142/S0217751X95000139

[17]

Remarks on higher Schwarzians

Anton Galajinsky
(
- Tomsk State U.
)

- Phys.Lett.B 843 (2023) 138042
•
e-Print:
- 2302.00317
•
DOI:
- 10.1016/j.physletb.2023.138042