Orientifold Singularities and Duality Ben Heidenreich (Harvard) with Iñaki García Etxebarria (MPI Munich) and Timm Wrase (Stanford SITP) 1210.7799, 1307.1701 and forthcoming
Review ( N = 4) AdS/CFT description: N D3s O3 (Witten '98) + H 3 ( S 5 / Z 2 , ˜ Z ) ∼ = Z 2 Montonen-Olive O 3 + : USp (2 k ) Duality B 2 O 3 − : τ → τ + 1 SO (2 k ) SO (2 k + 1) τ → − 1 / τ C 2 1/6
(BH, García-Etxebarria, Orbifolds ( N = 1) Wrase '12, '13) C 3 / Z 3 : z i → e 2 π i/ 3 z i σ : z i → − z i USp ( ˜ SO ( N − 4) N + 4) OR SU ( ˜ SU ( N ) N ) B 2 USp (2 k + 4) × SU (2 k ) { H 3 ( S 5 / Z 6 , ˜ Z ) ∼ = Z 2 Novel duality C 2 SO (2 k ) × SU (2 k + 4) SO (2 k − 1) × SU (2 k + 3) 2/6
Beyond Orbifolds dP 1 : x y z w C ∗ 2 2 − 1 − 3 Z 2 + − − − SU ( N − 4) SU ( N ) ± ⌥ SU ( ˜ SU ( ˜ N + 4) N ) ⌥ ⌥ 3/6
Discrete Torsion & Duality dP 1 ✓ S 3 × S 2 ◆ , ˜ H 3 ∼ Z = Z 2 ⊕ Z 2 Z 2 + B 2 τ → − 1 / τ IB + IB + IB − IB − IA − IA − IA + IA + τ → τ + 1 ? C 2 4/6
New Involutions from Deconfinement ( ) Seiberg Duality: Deconfinement: + flavors (Berkooz '95, Pouliot '95) New Involution! 5/6
New Orientifolds dP 1 SO ( N − 4) “Phase II”: SU ( N + F − 4) SU ( N ) + − − − SU ( F ) III + III + III − III − IB + IB + IB − IB − Anomalies, SCI, IA − IA − IA + IA + Low N examples ( − 1) N match! II + II + II − II − + + − − ( − 1) F 6/6
covariance requires additional orientifolds dP 1 SL (2 , Z ) IB + IB + IB − IB − ± ⌥ IA − IA − IA + IA + ⌥ ⌥ ? Constructed by deconfinement of parent theory + − − − Verified by strong duality checks III + III − III − III + IB + IB + IB − IB − IA − IA − IA + IA + II + II + II − II − + + − −
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