## Positivity, low twist dominance and CSDR for CFTs

Agnese Bissi, Aninda Sinha

SciPost Phys. 14, 083 (2023) · published 25 April 2023

- doi: 10.21468/SciPostPhys.14.4.083
- Submissions/Reports

### Abstract

We consider a crossing symmetric dispersion relation (CSDR) for CFT four point correlation with identical scalar operators, which is manifestly symmetric under the cross-ratios $u,v$ interchange. This representation has several features in common with the CSDR for quantum field theories. It enables a study of the expansion of the correlation function around $u=v=1/4$, which is used in the numerical conformal bootstrap program. We elucidate several remarkable features of the dispersive representation using the four point correlation function of $\Phi_{1,2}$ operators in 2d minimal models as a test-bed. When the dimension of the external scalar operator ($\Delta_\sigma$) is less than $\frac{1}{2}$, the CSDR gets contribution from only a single tower of global primary operators with the second tower being projected out. We find that there is a notion of low twist dominance (LTD) which, as a function of $\Delta_\sigma$, is maximized near the 2d Ising model as well as the non-unitary Yang-Lee model. The CSDR and LTD further explain positivity of the Taylor expansion coefficients of the correlation function around the crossing symmetric point and lead to universal predictions for specific ratios of these coefficients. These results carry over to the epsilon expansion in $4-\epsilon$ dimensions. We also conduct a preliminary investigation of geometric function theory ideas, namely the Bieberbach-Rogosinski bounds.

### Cited by 2

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}Agnese Bissi, -
^{2}Aninda Sinha

^{1}Uppsala universitet / Uppsala University^{2}भारतीय विज्ञान संस्थान / Indian Institute of Science Bangalore [IISc]

- Department of Science and Technology, Ministry of Science and Technology (through Organization: विज्ञान एवं प्रौद्योगिकी विभाग / Department of Science and Technology [DST])
- Knut och Alice Wallenbergs Stiftelse (Knut and Alice Wallenberg Foundation) (through Organization: Knut och Alice Wallenbergs Stiftelse / Knut and Alice Wallenberg Foundation)
- मानव संसाधन विकास मंत्रालय / Ministry of Human Resource Development [MHRD]
- Vetenskapsrådet / Swedish Research Council