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Unquenched Flavors in the Klebanov-Witten Model

Francesco Benini, Felipe Canoura, Stefano Cremonesi, Carlos Nunez, Alfonso V. Ramallo

TL;DR

This work constructs and analyzes a Type IIB supergravity background with unquenched, backreacting flavor D7-branes in the Klebanov-Witten setup by employing a near-continuous smearing of the flavor branes. It derives a tractable set of first-order BPS equations for the warped geometry, dilaton, and fluxes, and solves them to reveal a backreacted KW-like flow with a UV Landau pole and an IR regime approaching $AdS_5\times T^{1,1}$ up to logarithmic corrections; the flavor backreaction decouples in the deep IR. The paper then maps these geometric data to dual field theory quantities, obtaining holomorphic gauge couplings, beta-functions, and an $U(1)_R$ anomaly that matches the gravity description, and it discusses the role of massive flavors. In Part II, the authors generalize the smearing formalism to arbitrary Sasaki–Einstein $M_5$, derive a universal BPS system, present a superpotential formulation, and explore deformations and massive-flavor extensions, illustrating a broad and potentially universal framework for adding many flavors to ${\cal N}=1$ SCFTs from D3-branes at Calabi–Yau tips. The results offer a controlled setting to study Veneziano-like limits and flavor dynamics at strong coupling, with prospects for richer IR physics and UV completions in broader holographic contexts.

Abstract

Using AdS/CFT, we study the addition of an arbitrary number of backreacting flavors to the Klebanov-Witten theory, making many checks of consistency between our new Type IIB plus branes solution and expectations from field theory. We study generalizations of our method for adding flavors to all N=1 SCFTs that can be realized on D3-branes at the tip of a Calabi-Yau cone. Also, general guidelines suitable for the addition of massive flavor branes are developed.

Unquenched Flavors in the Klebanov-Witten Model

TL;DR

This work constructs and analyzes a Type IIB supergravity background with unquenched, backreacting flavor D7-branes in the Klebanov-Witten setup by employing a near-continuous smearing of the flavor branes. It derives a tractable set of first-order BPS equations for the warped geometry, dilaton, and fluxes, and solves them to reveal a backreacted KW-like flow with a UV Landau pole and an IR regime approaching up to logarithmic corrections; the flavor backreaction decouples in the deep IR. The paper then maps these geometric data to dual field theory quantities, obtaining holomorphic gauge couplings, beta-functions, and an anomaly that matches the gravity description, and it discusses the role of massive flavors. In Part II, the authors generalize the smearing formalism to arbitrary Sasaki–Einstein , derive a universal BPS system, present a superpotential formulation, and explore deformations and massive-flavor extensions, illustrating a broad and potentially universal framework for adding many flavors to SCFTs from D3-branes at Calabi–Yau tips. The results offer a controlled setting to study Veneziano-like limits and flavor dynamics at strong coupling, with prospects for richer IR physics and UV completions in broader holographic contexts.

Abstract

Using AdS/CFT, we study the addition of an arbitrary number of backreacting flavors to the Klebanov-Witten theory, making many checks of consistency between our new Type IIB plus branes solution and expectations from field theory. We study generalizations of our method for adding flavors to all N=1 SCFTs that can be realized on D3-branes at the tip of a Calabi-Yau cone. Also, general guidelines suitable for the addition of massive flavor branes are developed.

Paper Structure

This paper contains 28 sections, 202 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Generalities of the Procedure Used
  3. Organization of This Paper
  4. Part I: Adding Flavors to the Klebanov-Witten Field Theory
  5. What to Expect from Field Theory Considerations
  6. The Setup and the BPS Equations
  7. The Solution in Type IIB Supergravity
  8. Analysis of the Solution: Asymptotics and Singularities
  9. The Solution with $c_1=0$
  10. UV Limit
  11. IR Limit
  12. Detailed Study of the Dual Field Theory
  13. Holomorphic Gauge Couplings and $\beta$-functions
  14. R-symmetry Anomaly and Vacua
  15. The UV and IR Behaviors
  16. ...and 13 more sections

Figures (7)

  • Figure 1: We see on the left side the two stacks of $N_f$ flavor-branes localized on each of their respective $S^2$'s (they wrap the other $S^2$). The flavor group is clearly $U(N_f) \times U(N_f)$. After the smearing on the right side of the figure, this global symmetry is broken to $U(1)^{N_f - 1}\times U(1)^{N_f -1} \times U(1)_B \times U(1)_A$.
  • Figure 2: Quiver diagram of the Klebanov-Witten gauge theory with flavors. Circles are gauge groups while squares are non-dynamical flavor groups.
  • Figure 3: Unit cell of the lattice of Yang-Mills $\theta$ angles and RR fields integrals.
  • Figure 4: RG flow phase space for the Klebanov-Witten model.
  • Figure 5: Klebanov-Witten model with flavors. The A-C flow has backreacting D7's in the A piece and then follows the KW line in the C piece; it corresponds to $N_f \ll N_c$. The B flow is always far from the KW line, and corresponds to $N_f \gtrsim N_c$.
  • ...and 2 more figures