Guillaume Bossard, Charles CosnierHoreau, Boris Pioline
SciPost Phys. 3, 008 (2017) ·
published 31 July 2017

· pdf
Threedimensional string models with halfmaximal supersymmetry are believed
to be invariant under a large Uduality group which unifies the S and T
dualities in four dimensions. We propose an exact, Uduality invariant formula
for fourderivative scalar couplings of the form $F(\Phi) (\nabla\Phi)^4$ in a
class of string vacua known as CHL $\mathbb{Z}_N$ heterotic orbifolds with $N$
prime, generalizing our previous work which dealt with the case of heterotic
string on $T^6$. We derive the Ward identities that $F(\Phi)$ must satisfy, and
check that our formula obeys them. We analyze the weak coupling expansion of
$F(\Phi)$, and show that it reproduces the correct treelevel and oneloop
contributions, plus an infinite series of nonperturbative contributions.
Similarly, the large radius expansion reproduces the exact $F^4$ coupling in
four dimensions, including both supersymmetric invariants, plus infinite series
of instanton corrections from halfBPS dyons winding around the large circle,
and from TaubNUT instantons. The summation measure for dyonic instantons
agrees with the helicity supertrace for halfBPS dyons in 4 dimensions in all
charge sectors. In the process we clarify several subtleties about CHL models
in $D=4$ and $D=3$, in particular we obtain the exact helicity supertraces for
1/2BPS dyonic states in all duality orbits.
Submissions
Submissions for which this Contributor is identified as an author:
Prof. Pioline: "We appreciate the careful read..."
in Report on Exact effective interactions and 1/4BPS dyons in heterotic CHL orbifolds