Non-critical holography and four-dimensional CFT's with fundamentals

TL;DR

The paper develops non-critical string backgrounds in five and eight dimensions that holographically relate to 4D CFTs with fundamental matter, addressing the challenge of obtaining weakly curved critical duals for QCD-like theories. It constructs a 5D AdS solution with backreacted color and flavor branes on a linear dilaton background, providing a holographic model of conformal QCD with large $N_c$ and $N_f$, and analyzes flavor-brane fluctuations to explore the conformal window, noting the limitations from an order-one curvature. In eight dimensions, it derives a family of $AdS_5 \times \tilde{S}^3$ backgrounds sourced by color D3-branes and smeared flavor D5-branes on a KKL$_4$ base, with the internal squashed three-sphere controlled by a parameter $A$ solving a cubic in $Q_c^2/Q_f^2$, and identifies a special supersymmetric-like point at $Q_f/Q_c=\sqrt{2/3}$. The perturbation analysis around these AdS$_5 \times \tilde{S}^3$ backgrounds shows that the scalar/vector fluctuations have masses determined by $A$ and that the spectrum is stable within the explored parameter range, supporting the viability of non-critical AdS/CFT constructions and offering a pathway to flows toward the KKL$_4 vacuum. Together, the results illuminate how fundamental flavors can be encoded in non-critical holography, reveal a potential unique supersymmetric fixed point, and highlight the role of string corrections in extracting precise field-theory data such as conformal windows. The work thus provides qualitative insights into non-critical holographic duals of QCD-like theories and expands the set of AdS/CFT pairs with fundamental matter and reduced supersymmetry.

Abstract

We find non-critical string backgrounds in five and eight dimensions, holographically related to four-dimensional conformal field theories with N=0 and N=1 supersymmetries. In the five-dimensional case we find an AdS_5 background metric for a string model related to non-supersymmetric, conformal QCD with large number of colors and flavors and discuss the conjectured existence of a conformal window from the point of view of our solution. In the eight-dimensional string theory, we build a family of solutions of the form AdS_5 x \tilde{S}^3 with \tilde{S}^3 a squashed three-sphere. For a special value of the ratio N_f/N_c, the background can be interpreted as the supersymmetric near-horizon limit of a system of color and flavor branes on R^{1,3} times a known four-dimensional generalization of the cigar. The N=1 dual theory with fundamental matter should have an IR fixed point only for a fixed ratio N_f/N_c. General features of the string/gauge theory correspondence for theories with fundamental flavors are also addressed.