Universal RG flows across dimensions and holography

Self Cite

We study holographic renormalization group flows from four-dimensional N = 2 SCFTs to either N = 2 or N = 1 SCFTs. Our approach is based on the framework of five-dimensional half-maximal supergravity with general gauging, which we use to study domain wall solutions interpolating between different supersymmetric AdS 5 vacua. We show that a holographic RG flow connecting two N = 2 SCFTs is only possible if the flavor symmetry of the UV theory admits an SO(3) subgroup. In this case the ratio of the IR and UV central charges satisfies a universal relation which we also establish in field theory. In addition we provide several general examples of holographic flows from N = 2 to N = 1 SCFTs and relate the ratio of the UV and IR central charges to the conformal dimension of the operator triggering the flow. Instrumental to our analysis is a derivation of the general conditions for AdS vacua preserving eight supercharges as well as for domain wall solutions preserving eight Poincaré supercharges in half-maximal supergravity.

Section: Jhep06(2018)086supporting

confidence: 81%

Holographic RG flows for four-dimensional $$ \mathcal{N}=2 $$ SCFTs

Bobev

Triendl

2018

Self Cite

“…Further light on the relation between the 2d (0,4) CFTs dual to the AdS 3 solutions and compactifications on CY 2 of the 6d (1,0) CFTs dual to the AdS 7 solutions comes from comparing their respective central charges, following [62]. The holographic central charge of the 6d CFTs dual to the AdS 7 solutions was computed in [63]:…”

Section: Sive Iiamentioning

confidence: 99%

AdS3 solutions in massive IIA, defect CFTs and T-duality

Lozano

Macpherson

Núñez

et al. 2019

129

We establish a map between AdS 3 ×S 2 and AdS 7 solutions to massive IIA supergravity that allows one to interpret the former as holographic duals to D2-D4 defects inside 6d (1,0) CFTs. This relation singles out in a particular manner the AdS 3 ×S 2 solution constructed from AdS 3 ×S 3 ×CY 2 through non-Abelian T-duality, with respect to a freely acting SU(2). We find explicit global completions to this solution and provide well-defined (0,4) 2d dual CFTs associated to them. These completions consist of linear quivers with colour groups coming from D2 and D6 branes and flavour groups coming from D8 and D4 branes. Finally, we discuss the relation with flows interpolating between AdS 3 ×S 2 ×T 4 geometries and AdS 7 solutions found in the literature. 1 ylozano@uniovi.es 2

“…This is evidence that the compactified 4d N = 1 theories on these spaces do not flow to an IR fixed point. It would be of great interest to study the RG flow trajectories of the compactified 4d theories from first principles, e.g with field theoretical methods or holographic RG flow across dimensions as was done in [53].…”

Section: Discussionmentioning

confidence: 99%

“…(C. 53) We find that to get regular solutions we need c 2 > 0 and q > p > 0, i.e. to get x − < x + .…”

Section: C5 Solving the Regularity Equation And Matching To The Fielmentioning

confidence: 99%

Twisted $$ \mathcal{N} $$ = 1 SCFTs and their AdS3 duals

Couzens

Lam

Mayer

2020

We study compactifications of an infinite family of four-dimensional N = 1 SCFTs on a Riemann surface in the presence of arbitrary background fluxes for global symmetries. The four-dimensional parent theories have holographic Sasaki-Einstein duals in type IIB string theory. We compute central charges and R-charges of baryonic operators in the resulting twodimensional N = (0, 2) theories in three distinct ways: from the field theory side utilizing c-extremization, its recently discovered geometric dual formulation, and holographically using new AdS 3 duals of two-dimensional field theories. c.a.couzens@uu.nl h.hetlam@uu.nl k.mayer@uu.nl arXiv:1912.07605v2 [hep-th] 23 Dec 2019Since the advent of AdS/CFT in [1] many examples of dual pairs have been conjectured. The first (and most studied) was AdS 5 ×S 5 with five-form flux in type IIB and is proposed to be dual to four-dimensional N = 4 supersymmetric Yang-Mills [1]. The five-sphere can be replaced by an arbitrary five-dimensional Sasaki-Einstein manifold Y 5 and gives rise to AdS 5 ×Y 5 spaces dual to 4d N = 1 quiver gauge theories. In general, it is hard to find explicit metrics for these spaces and this makes it difficult to obtain evidence for new dualities. 1 Despite the difficulties, the infinite family of explicit Sasaki-Einstein metrics Y 5 = Y p,q [4] and its generalization Y 5 = L a,b,c [5] have been discovered. These manifolds are toric and specified by coprime integers p and q, and a, b and c respectively. The duality can be understood via its construction using D3-branes probing the Calabi-Yau cone singularity with base Y 5 . The 4d theory is the worldvolume theory on these D3-branes whilst AdS 5 × Y 5 is the near horizon geometry of the type IIB D3-brane solution.Of course, one can also study the correspondence in lower dimensions. One way is to take the aforementioned four-dimensional theories and compactify them on a (smooth) Riemann surface Σ g with genus g performing a topological twist to preserve supersymmetry. Additionally, background magnetic fluxes for the continuous flavour symmetries in the 4d theory can be turned on. Since these fluxes are quantized, every 4d theory leads to a discrete family of 2d theories. In the IR one expects these theories to flow to a 2d superconformal field theory (SCFT), however proving the existence of this flow is in general challenging. Assuming the existence of the SCFT one can compute its central charges and R-charges from UV data using the technique of c-extremization [6,7] which is based on anomaly considerations. In this scenario we are not considering a conventional RG flow from a 2d UV theory to the 2d IR theory but instead we consider an RG flow across dimensions. One can obtain evidence for the existence of the 2d SCFT using holography by finding an explicit supergravity solution with the same central charges and R-charges. Employing the D3-brane picture, one expects the solution to correspond to the near horizon geometry of a D3-brane compactified on the Riemann surface. This solution will be of the fo...