Hints of 5d Fixed Point Theories from Non-Abelian T-duality

In this paper we investigate the properties of the putative 5d fixed point theory that should be dual, through the holographic correspondence, to the new supersymmetric AdS(6) solution constructed in Lozano et al. This solution is the result of a non-Abelian T-duality transformation on the known supersymmetric AdS(6) solution of massive Type IIA. The analysis of the charge quantization conditions seems to put constraints on the global properties of the background, which, combined with the information extracted from considering probe branes, suggests a 2-node quiver candidate for the dual CFT.

• The string theory realization is only known for very specific cases 2. The D4-D8 system (Seiberg'96) N f < 8 5d SUSY fixed points with E N f +1 global symmetry can be obtained in the infinite bare coupling limit of N=1 SYM with gauge group Sp(N), one antisymmetric hypermultiplet and fundamental hypermultiplets martes 5 de agosto de 2014 2. The D4-D8 system (Seiberg'96) N f < 8 5d SUSY fixed points with E N f +1 global symmetry can be obtained in the infinite bare coupling limit of N=1 SYM with gauge group Sp(N), one antisymmetric hypermultiplet The theory can be engineered in Type I' ST on a stack of N D4-branes probing a O8 − plane with N f D8-branes and fundamental hypermultiplets martes 5 de agosto de 2014 2. The D4-D8 system (Seiberg'96) N f < 8 5d SUSY fixed points with E N f +1 global symmetry can be obtained in the infinite bare coupling limit of N=1 SYM with gauge group Sp(N), one antisymmetric hypermultiplet A D4-brane probe in the D8-O8 background metric has a gauge coupling z i : locations of the 16 D8-branes (Brandhuber,Oz'99;Ferrara,Kehagias,Partouche,Zaffaroni'98) A D4-brane probe in the D8-O8 background metric In the field theory limit ( l s → 0 + gauge coupling fixed): s has a gauge coupling Then: This reproduces the effective gauge coupling of the 5d Sp(N) gauge theory with 16 fundamental hypers with masses and one massless antisym. hypermultiplet (Seiberg'96) Then: This reproduces the effective gauge coupling of the 5d Sp(N) gauge theory with 16 fundamental hypers with masses and one massless antisym. hypermultiplet (Seiberg'96)

Taking massless hypermultiplets:
N f one gets: -For N f > 8 , g 2 becomes negative at some point in the moduli space → Sick theory implies that: implies that: at the origin of the Coulomb branch implies that: at the origin of the Coulomb branch Here the global symmetry of the theory: The field theory calculation can be generalized to other gauge groups and matter content (Intriligator, Morrison, Seiberg'97) implies that: at the origin of the Coulomb branch , which lack however an AdS/CFT description Here the global symmetry of the theory: The near horizon geometry of the D4-D8 system is a fibration of AdS 6 over half-S 4 with an boundary at the ds 2 = W 2 L 2 4 9 ds 2 (AdS 6 ) + 4 ds 2 (S 4 ) position of the O8-plane, preserving 16 SUSYs The near horizon geometry of the D4-D8 system is a fibration of AdS 6 over half-S 4 with an boundary at the • symmetry broken to : R-symmetry of the field theory global symmetry massless antisym. hyper position of the O8-plane, preserving 16 SUSYs The near horizon geometry of the D4-D8 system is a fibration of AdS 6 over half-S 4 with an boundary at the • symmetry broken to : R-symmetry of the field theory global symmetry massless antisym. hyper In the presence of an Abelian isometry: Go to adapted coordinates: X µ = {θ, X α } such that θ → θ + and ∂ θ (backgrounds) = 0 Buscher's formulae  Non-Abelian T-duality (De la Ossa,Quevedo'93) Non-Abelian continuous isometry: ii) Add a Lagrange multiplier term: Tr(χF ) Hassan'99: Implement the relative twist between left and right movers in the bispinor formed by the RR fields: Same thing in the non-Abelian case (Sfetsos,Thompson'10) 4. Non-Abelian T-duality as a solution generating technique:

Interesting new solutions have been found with CFT duals
But what if NATD is not a symmetry of ST?

The non-Abelian T-dual of Brandhuber and Oz
6. Hints on the 5d dual CFT i) Quantization of charges: and depend on the large gauge transf. of (which seems, on the other hand, to undergo something reminiscent of the cascade in KS), in such a way that they cannot be integers for all (r, θ) martes 5 de agosto de 2014 6. Hints on the 5d dual CFT i) Quantization of charges: and depend on the large gauge transf. of (which seems, on the other hand, to undergo something reminiscent of the cascade in KS), in such a way that they cannot be integers for all (r, θ) This fixes the maximum value of r to r = π ii) Probe the Coulomb branch: 2 directions BPS D5 and D7 branes Fluctuations of these branes: ii) Probe the Coulomb branch: 2 directions BPS D5 and D7 branes Fluctuations of these branes:

D5:
Consistently, we should find a wrapped brane with a tadpole given by the CS coefficient: ↔ , D1-brane wrapped on : A t r martes 5 de agosto de 2014 ii) Probe the Coulomb branch: 2 directions BPS D5 and D7 branes Fluctuations of these branes:

D5:
Consistently, we should find a wrapped brane with a tadpole given by the CS coefficient: ii) Baryon-like operators: Dual to branes wrapped on the internal geometry with a tadpole proportional to the rank of the gauge group In the D4-D8 background: D4-brane with N charge, projected out by the orbifold In the non-Abelian dual: D1-brane with N θ 7 charge plus D3-brane (wrapped on S 2 ) with N θ 5 charge Projected out by the dual orbifold In any case they inform about the ranks of the dual gauge groups iv) Putting it all together: We seem to have two gauge groups with ranks N θ 7 , N θ 5 and flavor symmetries N r 5 , N r 7 actually zero, such that the background is globally N θ 5 well defined Manifestation in the CFT of a perfectly regular background terminating at a point?