N = 2 type II-heterotic duality and higher-derivative F-terms

Abstract

We test the recently conjectured duality between N =2 supersymmetric type II and heterotic string models by analysing a class of higher dimensional interactions in the respective low-energy Lagrangians. These are F -terms of the form F g W 2g where W is the gravitational superfield. On the type II side these terms are generated at the g-loop level and in fact are given by topological partition functions of the twisted Calabi-Yau sigma model. We show that on the heterotic side these terms arise at the one-loop level. We study in detail a rank 3 example and show that the corresponding couplings F g satisfy the same holomorphic anomaly equations as in the type II case.Moreover we study the leading singularities of F g 's on the heterotic side, near the enhanced symmetry point and show that they are universal poles of order 2g−2 with coefficients that are given by the Euler number of the moduli space of genus-g Riemann surfaces. This confirms a recent conjecture that the physics near conifold singularity is governed by c=1 string theory at the self-dual point.

Heterotic — type I superstring duality and low-energy effective actions

“…1 Similar tests of heterotic-type II string duality [6,1] in six and four dimensions were done in [7] and [8].…”

“…This implies that though there may be higher-derivative corrections, F 4 will not be renormalised. 8 Since the field strengths contain non-linear commutator terms and the curvature terms expanded near flat space contain terms of all orders in h µν , the gauge invariance implies similar non-renormalisation of certain low-momentum terms in infinite sets of vector and graviton amplitudes.…”

“…7 This is an interesting new example of a D = 10 'nonrenormalisation theorem' which applies to terms originating from certain 4-point string amplitudes. 8 This non-renormalisation allows one to extend the duality relation between the leading terms in the type I and heterotic string effective actions to those higher-derivative terms. 7 A close connection between the calculation of the anomaly index and the one-loop O(R 4 , R 2 F 2 , F 4 ) term represented as a torus partition function in a background was suggested as an indication that this term should not receive higher heterotic string loop corrections [23].…”

Instanton numbers and exchange symmetries in N = 2 dual string pairs

“…The higher derivative couplings of vector multiplets X to the Weyl multiplet W of conformal N = 2 supergravity can be expressed as a power series [21,22] …”

The symplectic structure of N=2 supergravity and its central extension

“…Exact solutions of the infrared regime of both N = 2 super Yang-Mills theories [1,2] and their string analogue [9] have been the subject of intensive investigation over the last year [10] , and spectacular results [11][12][13][14] substantiating proposed assumptions about the exact solutions have been obtained.…”