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Four-derivative couplings and BPS dyons in heterotic CHL orbifolds
by Guillaume Bossard, Charles Cosnier-Horeau, Boris Pioline
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Boris Pioline |
| Submission information | |
|---|---|
| Preprint Link: | http://arxiv.org/abs/1702.01926v3 (pdf) |
| Date submitted: | 2017-05-08 02:00 |
| Submitted by: | Pioline, Boris |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Three-dimensional string models with half-maximal supersymmetry are believed to be invariant under a large U-duality group which unifies the S and T dualities in four dimensions. We propose an exact, U-duality invariant formula for four-derivative 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 tree-level and one-loop contributions, plus an infinite series of non-perturbative 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 half-BPS dyons winding around the large circle, and from Taub-NUT instantons. The summation measure for dyonic instantons agrees with the helicity supertrace for half-BPS 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 1/2-BPS dyonic states in all duality orbits.
Author comments upon resubmission
List of changes
- In abstract, replaced "NS5-brane, Kaluza-Klein monopole and H-monopole instantons" by "non-perturbative contributions".
- At end of abstract, added "in particular we obtain the exact helicity supertraces for 1/2-BPS dyonic states in all duality orbits."
- Clarified the discussion of the U-duality 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 U-duality 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 one-loop 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 $\Lambda_{p-1,q-1}$ by $\Lambda_{p-2,q-2}$ 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
Published as SciPost Phys. 3, 008 (2017)