Positivity, low twist dominance and CSDR for CFTs

• We consider a crossing symmetric dispersion relation (CSDR) for CFT four point correla-tion 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 1 the dimension of the external scalar operator ( increment sigma) is less than 2 , the CSDR gets con-tribution 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 increment 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.

Ämnesord

NATURVETENSKAP  -- Fysik -- Subatomär fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences -- Subatomic Physics (hsv//eng)

Publikations- och innehållstyp

ref (ämneskategori)

art (ämneskategori)