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Fourderivative couplings and BPS dyons in heterotic CHL orbifolds
by Guillaume Bossard, Charles CosnierHoreau, Boris Pioline
 Published as SciPost Phys. 3, 008 (2017)
Submission summary
As Contributors:  Boris Pioline 
Arxiv Link:  http://arxiv.org/abs/1702.01926v3 (pdf) 
Date submitted:  20170508 02:00 
Submitted by:  Pioline, Boris 
Submitted to:  SciPost Physics 
Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
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.
Ontology / Topics
See full Ontology or Topics database.Published as SciPost Phys. 3, 008 (2017)
Author comments upon resubmission
List of changes
 In abstract, replaced "NS5brane, KaluzaKlein monopole and Hmonopole instantons" by "nonperturbative contributions".
 At end of abstract, added "in particular we obtain the exact helicity supertraces for 1/2BPS dyonic states in all duality orbits."
 Clarified the discussion of the Uduality group $G_4(Z)$, starting 4 lines before eq (2.2) up until 2 lines above eq (2.6).
 Replaced $q$ by $q_S=e^{2\pi i S}$ in (2.5)
 Above (2.14), added references [24,25] to Dabholkar et al (2005) and Sen (2005)
 Defined $q=e^{2\pi i \tau}$ below (2.14)
 Clarified the discussion of the Uduality group $G_3(Z)$, starting below eq (2.19) up until eq (2.22).
 removed footnote 5, along with the sentence "(which can be viewed as a oneloop corrected mass formula)" and the former reference [29]
 Restored missing index $J$ in (3.11)
 Replaced $Q$ by $\widetilde{Q}$ in (4.8)
 Explicited the integration domain In Eq (4.24), (4.29), (5.18), (5.28), (5.42)
 Rewrote sentences around (4.36)
 Removed the unwanted sum of $\widetilde{Q}$ in (5.9), and replaced $\Lambda_{p1,q1}$ by $\Lambda_{p2,q2}$ in that same equation
 Third bullet on page 33 (starting with "The remaining contributions A with $(n_2,m_2)=(0,0)$...) moved into main text
 Rewrote the sentence below (5.33)
 Added "heterotic" in the title of Appendix A
 Corrected various misprints pointed out by the referees