Evidence for the Strongest Version of the 4d a-Theorem, via a-Maximization Along RG Flows

Abstract

In earlier work, we (KI and BW) gave a two line "almost proof" (for supersymmetric RG flows) of the weakest form of the conjectured 4d a-theorem, that a_{IR}<a_{UV}, using our result that the exact superconformal R-symmetry of 4d SCFTs maximizes a=3Tr R^3-Tr R. The proof was incomplete because of two identified loopholes: theories with accidental symmetries, and the fact that it's only a local maximum of \it{a}. Here we discuss and extend a proposal of Kutasov (which helps close the latter loophole) in which a-maximization is generalized away from the endpoints of the RG flow, with Lagrange multipliers that are conjectured to be identified with the running coupling constants. a-maximization then yields a monotonically decreasing "a-function" along the RG flow to the IR. As we discuss, this proposal in fact suggests the strongest version of the a-theorem: that 4d RG flows are gradient flows of an a-function, with positive definite metric. In the perturbative limit, the RG flow metric thus obtained is shown to agree precisely with that found by very different computations by Osborn and collaborators. As examples, we discuss a new class of 4d SCFTs, along with their dual descriptions and IR phases, obtained from SQCD by coupling some of the flavors to added singlets.

36 pages, 6 figures. v2: added reference

References in corpus (25)

• Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories
• New Phenomena in SU(3) Supersymmetric Gauge Theory
• The Exact Superconformal R-Symmetry Maximizes a
• New N=2 Superconformal Field Theories in Four Dimensions
• Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories
• Positivity Constraints on Anomalies in Supersymmetric Gauge Theories
• N=1 Superconformal Symmetry in Four Dimensional Quantum Field Theory
• Scheme dependence and the NSVZ $\beta$-function
• Central Charges and $U(1{)}_R$ Symmetries in $\mathcal{N}=1$ Super Yang-Mills
• $N=1$ supersymmetry and the three loop anomalous dimension for the chiral superfield
• Sasaki-Einstein Metrics on S^2 x S^3
• A Critical Behaviour of Anomalous Currents, Electric-Magnetic Universality and CFT_4
• Chaotic Duality in String Theory
• Correlation Functions of the Energy Momentum Tensor on Spaces of Constant Curvature
• Dibaryons from Exceptional Collections
• RG Fixed Points and Flows in SQCD with Adjoints
• A proof of the irreversibility of renormalization group flows in four dimensions
• New Results on the "$a$-theorem" in Four Dimensional Supersymmetric Field Theory
• Lagrange Multipliers and Couplings in Supersymmetric Field Theory
• A Note on the Holographic Beta and C Functions
• Matching Conditions and Duality in N=1 SUSY Gauge Theories in the Conformal Window
• Baryon Charges in 4d Superconformal Field Theories and Their AdS Duals
• Constructing a c-function for SUSY Gauge Theories
• A Mixed Phase of SUSY Gauge Theories from a-Maximization
• Inequalities for trace anomalies, length of the RG flow, distance between the fixed points and irreversibility

Cited by in corpus (101)

• Towards a derivation of holographic entanglement entropy
• Holographic c-theorems in arbitrary dimensions
• The Exact Superconformal R-Symmetry Extremizes Z
• Gauge Theories from Toric Geometry and Brane Tilings
• Black hole microstates in AdS${}_4$ from supersymmetric localization
• An Infinite Family of Superconformal Quiver Gauge Theories with Sasaki-Einstein Duals
• Entanglement entropy: holography and renormalization group
• Bounds on 4D Conformal and Superconformal Field Theories
• Supersymmetry on Curved Spaces and Holography
• Comments on Holographic Entanglement Entropy and RG Flows
• Exactly Marginal Deformations and Global Symmetries
• New checks and subtleties for AdS/CFT and a-maximization
• On renormalization group flows and the a-theorem in 6d
• Conformal Windows of SU(N) Gauge Theories, Higher Dimensional Representations and The Size of The Unparticle World
• Constraints on RG Flow for Four Dimensional Quantum Field Theories
• Dynamical SUSY Breaking at Meta-Stable Minima from D-branes at Obstructed Geometries
• Compactifications of the Klebanov-Witten CFT and new $Ad{S}_3$ backgrounds
• Easy Dirac Gauginos
• Lagrange Multipliers and Couplings in Supersymmetric Field Theory
• Conformally Sequestered SUSY Breaking in Vector-like Gauge Theories
• Comments on scaling limits of 4d N=2 theories
• Constraints on 3- and 4-loop $\beta$-functions in a general four-dimensional Quantum Field Theory
• Nonperturbative Renormalization of Operators in Near-Conformal Systems Using Gradient Flows
• Direct Gaugino Mediation
• The Exact Superconformal R-symmetry Minimizes ${\tau }_{RR}$
• Higher Representations: Confinement and Large N
• Gapped Chiral Fermions
• Consequences of Weyl Consistency Conditions
• c-theorem of the entanglement entropy
• Defect $a$-Theorem and $a$-Maximization
• Scale without Conformal Invariance: Theoretical Foundations
• Limit Cycles in Four Dimensions
• Counting RG flows
• N=1 RG Flows, Product Groups, and a-Maximization
• R-charges, Chiral Rings and RG Flows in Supersymmetric Chern-Simons-Matter Theories
• Quantum Information Scrambling: From Holography to Quantum Simulators
• Index for Supergravity on AdS_5 \times T^{1,1} and Conifold Gauge Theory
• More on Conformally Sequestered SUSY Breaking
• A Crack in the Conformal Window
• Comments on a-maximization from gauged supergravity
• Holographic c-theorems and higher derivative gravity
• The a-function for gauge theories
• New N=1 dualities from orientifold transitions - Part II: String Theory
• New N=1 dualities from orientifold transitions - Part I: Field Theory
• A counterexample to the a-'theorem'
• New results on superconformal quivers
• F-maximization along the RG flows: a proposal
• Refined Checks and Exact Dualities in Three Dimensions
• Superconformal Flavor Simplified
• Weakly coupled conformal manifolds in 4d
• A new Ricci flat geometry
• Two-loop renormalization of multiflavor ${\varphi }^3$ theory in six dimensions and the trace anomaly
• Conformal Gauge Mediation and Light Gravitino of Mass m_{3/2} <O(10) eV
• Classification of large N superconformal gauge theories with a dense spectrum
• The a-function in three dimensions: beyond leading order
• An Attractor for Natural Supersymmetry
• Single-sector supersymmetry breaking, chirality, and unification
• Duality and Transport for Supersymmetric Graphene from the Hemisphere Partition Function
• Comments on scale invariant but non-conformal supersymmetric field theories
• Notes on Integral Identities for 3d Supersymmetric Dualities
• Comments on Worldsheet Description of the Omega Background
• A holographic c-theorem for higher derivative gravity
• Phases of N=1 supersymmetric chiral gauge theories
• Bounds on SCFTs from Conformal Perturbation Theory
• Infinitely many 4d N=1 SCFTs with a=c
• Unitarity bounds and RG flows in time dependent quantum field theory
• Pouliot Type Duality via a-Maximization
• A Conformal Gauge Mediation and Dark Matter with Only One Parameter
• On the exact R charge for N=2 CS theories
• Simple Models of Superconformal Flavor
• Space-time dependent couplings in N=1 SUSY gauge theories: Anomalies and Central Functions
• Metastable Vacua in Superconformal SQCD-like Theories
• (Delta a) curiosities in some 4d susy RG flows
• Semi-direct Gauge-Yukawa Mediation
• New dynamics and dualities in supersymmetric chiral gauge theories
• Electric/Magnetic Duality with Gauge Singlets
• a-Maximization, Global Symmetries and RG Flows
• Holographic $T\bar{T}$ deformation of the entanglement entropy in (A)dS${}_3$/CFT${}_2$
• Comments on Bounds on Central Charges in N=1 Superconformal Theories
• S-duality of nonsupersymmetric gauge theories
• 3D ${\tau }_{RR}$-minimization in AdS${}_4$ gauged supergravity
• A test for emergent dynamics
• Higgsing and Superpotential Deformations of ADE Superconformal Theories
• The Phase Structure of Supersymmetric Sp(2N_c) Gauge Theories with an Adjoint
• Scheme Dependence and Multiple Couplings
• Generalized symmetry constraints on deformed 4d (S)CFTs
• Holographic duality and applications
• RG Flows and Dynamical Systems
• Searching for a $C$-function on the three-dimensional sphere
• Strong gauging or decoupling ghost matter
• New self dualities and duality cascades
• A landscape of 4d N=1 SCFTs with a=c
• $c_{\mathrm{eff}}$ from Resurgence at the Stokes Line
• Comments on asymptotic safety in four-dimensional $\mathcal{N}=1$ supersymmetric gauge theories
• Aspects of 4d supersymmetric dynamics and geometry
• Emergent Supersymmetry in the Marginal Deformations of N=4 SYM
• Series of Tests of a Constraint on Asymptotically Free Gauge Theories
• A three-loop check of the 'a - maximization' in SQCD with adjoint(s)
• a-Maximization in N=1 Supersymmetric Spin(10) Gauge Theories
• Dual RG flows in 4D
• On the Chiral Ring and Vacua of $\mathcal{N}=1$ Adjoint SQCD