Abstract
We consider D3 branes in presence of an S-fold plane. The latter is a non-perturbative object, arising from the combined projection of an S-duality twist and a discrete orbifold of the R-symmetry group. This construction naively gives rise to 4d \( \mathcal{N} \) = 3 SCFTs. Nevertheless it has been observed that in some cases supersymmetry is enhanced to \( \mathcal{N} \) = 4. In this paper we study the explicit counting of degrees of freedom arising from vector multiplets associated to strings suspended between the D3 branes probing the S-fold. We propose that, for trivial discrete torsion, there is no vector multiplet associated to (1, 0) strings stretched between a brane and its image. We then focus on the case of rank 2 \( \mathcal{N} \) = 3 theory that enhances to SU(3) \( \mathcal{N} \) = 4 SYM, explicitly spelling out the isomorphism between the BPS-spectrum of the manifestly \( \mathcal{N} \) = 3 theory and that of three D3 branes in flat spacetime. Subsequently, we consider 3-pronged strings in these setups and show how wall-crossing in the S-fold background implies wall crossing in the flat geometry. This can be considered a consistency check of the conjectured SUSY enhancement. We also find that the above isomorphism implies that a (1, 0) string, suspended between a brane and its image in the S-fold, corresponds to a 3-string junction in the flat geometry. This is in agreement with our claim on the absence of a vector multiplet associated to such (1, 0) strings. This is because the 3-string junction in flat geometry gives rise to a 1/4-th BPS multiplet of the \( \mathcal{N} \) = 4 algebra. Such multiplets always include particles with spin > 1 as opposed to a vector multiplet which is restricted by the requirement that the spins must be ≤ 1.
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References
O. Aharony and M. Evtikhiev, On four dimensional N = 3 superconformal theories, JHEP 04 (2016) 040 [arXiv:1512.03524] [INSPIRE].
I. Garcia-Etxebarria and D. Regalado, \( \mathcal{N} \) = 3 four dimensional field theories, JHEP 03 (2016) 083 [arXiv:1512.06434] [INSPIRE].
S. Ferrara, M. Porrati and A. Zaffaroni, N=6 supergravity on AdS 5 and the SU(2,2/3) superconformal correspondence, Lett. Math. Phys. 47 (1999) 255 [hep-th/9810063] [INSPIRE].
S.W. Beck, J.B. Gutowski and G. Papadopoulos, AdS 5 backgrounds with 24 supersymmetries, JHEP 06 (2016) 126 [arXiv:1601.06645] [INSPIRE].
C. Cordova, T.T. Dumitrescu and K. Intriligator, Deformations of Superconformal Theories, arXiv:1602.01217 [INSPIRE].
T. Nishinaka and Y. Tachikawa, On 4d rank-one N = 3 superconformal field theories, arXiv:1602.01503 [INSPIRE].
P.C. Argyres, M. Lotito, Y. Lü and M. Martone, Expanding the landscape of \( \mathcal{N} \) = 2 rank 1 SCFTs, JHEP 05 (2016) 088 [arXiv:1602.02764] [INSPIRE].
O. Aharony and Y. Tachikawa, S-folds and 4d N = 3 superconformal field theories, JHEP 06 (2016) 044 [arXiv:1602.08638] [INSPIRE].
D.R. Morrison and C. Vafa, F-theory and \( \mathcal{N} \) = 1 SCFTs in four dimensions, JHEP 08 (2016) 070 [arXiv:1604.03560] [INSPIRE].
Y. Imamura, H. Kato and D. Yokoyama, Supersymmetry Enhancement and Junctions in S-folds, arXiv:1606.07186 [INSPIRE].
C.M. Hull, A Geometry for non-geometric string backgrounds, JHEP 10 (2005) 065 [hep-th/0406102] [INSPIRE].
A. Dabholkar, String compactifications: old and new, in On recent developments in theoretical and experimental general relativity, gravitation, and relativistic field theories, proceedings of the 10th Marcel Grossmann Meeting, MG10, Rio de Janeiro, Brazil, 20-26 July 2003, pg. 148-164.
L. Nilse, Classification of 1D and 2D orbifolds, AIP Conf. Proc. 903 (2007) 411 [hep-ph/0601015] [INSPIRE].
E. Witten, Baryons and branes in anti-de Sitter space, JHEP 07 (1998) 006 [hep-th/9805112] [INSPIRE].
G.C. Shephard, Regular complex polytopes, Proc. London Math. Soc. s3-2 (1952) 82 [http://plms.oxfordjournals.org/content/s3-2/1/82.full.pdf+html].
G. Shephard, Unitary groups generated by reflections, Canad. J. Math 5 (1953) 364.
G.C. Shephard and J.A. Todd, Finite unitary reflection groups, Canad. J. Math 6 (1954) 274.
O. Bergman, Three pronged strings and 1/4 BPS states in N = 4 super Yang-Mills theory, Nucl. Phys. B 525 (1998) 104 [hep-th/9712211] [INSPIRE].
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ArXiv ePrint: 1607.00313
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Agarwal, P., Amariti, A. Notes on S-folds and \( \mathcal{N} \) = 3 theories. J. High Energ. Phys. 2016, 32 (2016). https://doi.org/10.1007/JHEP09(2016)032
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DOI: https://doi.org/10.1007/JHEP09(2016)032