arXiv subjects

Ken Intriligator

Publications and source records attributed to Ken Intriligator.

18 recordsLinked to original sources

arXiv2005

The Exact Superconformal R-symmetry Minimizes $τ_{RR}$

We present a new, general constraint which, in principle, determines the superconformal $U(1)_R$ symmetry of 4d $\N =1$ SCFTs, and also 3d $\N =2$ SCFTs. Among all possibilities, the superconformal $U(1)_R$ is that which minimizes the coefficient, $τ_{RR}$, of its two-point function. Equivalently, the superconformal $U(1)_R$ is the unique one with vanishing two-point function with every non-R flavor symmetry. For 4d $\N =1$ SCFTs, $τ_{RR}$ minimization gives an alternative to a-maximization. $τ_{RR}$ minimization also applies in 3d, where no condition for determining the superconformal $U(1)_R$ had been previously known. Unfortunately, this constraint seems impractical to implement for interacting field theories. But it can be readily implemented in the AdS geometry for SCFTs with AdS duals.

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arXiv2005

Current Correlators and AdS/CFT Geometry

We consider current-current correlators in 4d $\N =1$ SCFTs, and also 3d $\N =2$ SCFTs, in connection with AdS/CFT geometry. The superconformal $U(1)_R$ symmetry of the SCFT has the distinguishing property that, among all possibilities, it minimizes the coefficient, $τ_{RR}$ of its two-point function. We show that the geometric Z-minimization condition of Martelli, Sparks, and Yau precisely implements $τ_{RR}$ minimization. This gives a physical proof that Z-minimization in geometry indeed correctly determines the superconformal R-charges of the field theory dual. We further discuss and compare current two point functions in field theory and AdS/CFT and the geometry of Sasaki-Einstein manifolds. Our analysis gives new quantitative checks of the AdS/CFT correspondence.

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arXiv2005

N=1 RG Flows, Product Groups, and a-Maximization

We explore new IR phenomena and dualities, arising for product groups, in the context of N=1 supersymmetric gauge theories. The RG running of the multiple couplings can radically affect each other. For example, an otherwise IR interacting coupling can be driven to be instead IR free by an arbitrarily small, but non-zero, initial value of another coupling. Or an otherwise IR free coupling can be driven to be instead IR interacting by an arbitrarily small non-zero initial value of another coupling. We explore these and other phenomena in N=1 examples, where exact results can be obtained using a-maximization. We also explore the various possible dual gauge theories, e.g. by dualizing one gauge group with the other treated as a weakly gauged flavor symmetry, along with previously proposed duals for the theories deformed by A_k-type Landau-Ginzburg superpotentials. We note that this latter duality, and all similar duality examples, always have non-empty superconformal windows, within which both the electric and dual A_k superpotentials are relevant.

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arXiv2004

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

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.

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arXiv2004

Exploring the 4d Superconformal Zoo

We discuss a new constraint for determining the superconformal U(1)_R symmetry of 4d N=1 SCFTs: It is the unique one which locally maximizes a(R) = 3Tr R^3-Tr R. This constraint comes close to proving the conjectured "a-theorem" for N=1 SCFTs. Using this "a-maximization", exact results can now be obtained for previously inaccessible 4d N=1 SCFTs. We apply this method to a rich class of examples: 4d N=1 SQCD with added matter chiral superfields in the adjoint representation. We classify a zoo of SCFTs, finding that Arnold's ADE singularity classification arises in classifying these theories via all possible relevant Landau-Ginzburg superpotentials. We verify that all RG flows are indeed compatible with the "a-theorem" conjecture, a_{IR}<a_{UV}, in every case

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arXiv2003

On Low Rank Classical Groups in String Theory, Gauge Theory and Matrix Models

We consider N=1 supersymmetric U(N), SO(N), and Sp(N) gauge theories, with two-index tensor matter and added tree-level superpotential, for general breaking patterns of the gauge group. By considering the string theory realization and geometric transitions, we clarify when glueball superfields should be included and extremized, or rather set to zero; this issue arises for unbroken group factors of low rank. The string theory results, which are equivalent to those of the matrix model, refer to a particular UV completion of the gauge theory, which could differ from conventional gauge theory results by residual instanton effects. Often, however, these effects exhibit miraculous cancellations, and the string theory or matrix model results end up agreeing with standard gauge theory. In particular, these string theory considerations explain and remove some apparent discrepancies between gauge theories and matrix models in the literature.

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arXiv2003

The Glueball Superpotential

We compute glueball superpotentials for four-dimensional, N=1 supersymmetric gauge theories, with arbitrary gauge groups and massive matter representations. This is done by perturbatively integrating out massive, charged fields. The Feynman diagram computations simplify, and are related to the corresponding matrix model. This leads to a natural notion of ``projection to planar diagrams'' for arbitrary gauge groups and representations. We discuss a general ambiguity in the glueball superpotential W(S) for terms, S^n, whose order, n, is greater than the dual Coxeter number. This ambiguity can be resolved for all classical gauge groups, (A,B,C,D), via a natural embedding in an infinite rank supergroup. We use this to address some recently raised puzzles. For exceptional groups, we compute the superpotential terms for low powers of the glueball field and propose an all-order completion for some examples including N=1^* for all simply-laced groups. We also comment on compactification of these theories to lower dimensions.

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arXiv2003

RG Fixed Points and Flows in SQCD with Adjoints

We map out and explore the zoo of possible 4d N=1 superconformal theories which are obtained as RG fixed points of N=1 SQCD with N_f fundamental and N_a adjoint matter representations. Using "a-maximization," we obtain exact operator dimensions at all RG fixed points and classify all relevant, Landau-Ginzburg type, adjoint superpotential deformations. Such deformations can be used to RG flow to new SCFTs, which are then similarly analyzed. Remarkably, the resulting 4d SCFT classification coincides with Arnold's ADE singularity classification. The exact superconformal R-charge and the central charge a are computed for all of these theories. RG flows between the different fixed points are analyzed, and all flows are verified to be compatible with the conjectured a-theorem.

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arXiv2003

The Exact Superconformal R-Symmetry Maximizes a

An exact and general solution is presented for a previously open problem. We show that the superconformal R-symmetry of any 4d SCFT is exactly and uniquely determined by a maximization principle: it is the R-symmetry, among all possibilities, which (locally) maximizes the combination of 't Hooft anomalies a_{trial}(R) \equiv (9 Tr R^3-3 Tr R)/32. The maximal value of a_{trial} is then, by a result of Anselmi et. al., the central charge \it{a} of the SCFT. Our a_{trial} maximization principle almost immediately ensures that the central charge \it{a} decreases upon any RG flow, since relevant deformations force a_{trial} to be maximized over a subset of the previously possible R-symmetries. Using a_{trial} maximization, we find the exact superconformal R-symmetry (and thus the exact anomalous dimensions of all chiral operators) in a variety of previously mysterious 4d N=1 SCFTs. As a check, we verify that our exact results reproduce the perturbative anomalous dimensions in all perturbatively accessible RG fixed points. Our result implies that N =1 SCFTs are algebraic: the exact scaling dimensions of all chiral primary operators, and the central charges \it{a} and \it{c}, are always algebraic numbers.

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arXiv2003

Baryon Charges in 4d Superconformal Field Theories and Their AdS Duals

We consider general aspects of the realization of R and non-R flavor symmetries in the AdS_5 x H_5 dual of 4d N=1 superconformal field theories. We find a general prescription for computing the charges under these symmetries for baryonic operators, which uses only topological information (intersection numbers) on H_5. We find and discuss a new correspondence between the nodes of the SCFT quiver diagrams and certain divisors in the associated geometry. We also discuss connections between the non-R flavor symmetries and the enhanced gauge symmetries in non-conformal theories obtained by adding wrapped branes.

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arXiv2002

*-Wars Episode I: The Phantom Anomaly

As pointed out, chiral non-commutative theories exist, and examples can be constructed via string theory. Gauge anomalies require the matter content of individual gauge group factors, including U(1) factors, to be non-chiral. All ``bad'' mixed gauge anomalies, and also all ``good'' (e.g. for $π^0\to γγ$) ABJ type flavor anomalies, automatically vanish in non-commutative gauge theories. We interpret this as being analogous to string theory, and an example of UV/IR mixing: non-commutative gauge theories automatically contain ``closed string,'' Green-Schwarz fields, which cancel these anomalies.

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arXiv2001

The Secret Gauging of Flavor Symmetries in Noncommutative QFT

We show that flavor 't Hooft anomalies automatically vanish in noncommutative field theories which are obtained from string theory in the decoupling limit. We claim that this is because the flavor symmetries are secretly local, because of coupling to closed string bulk modes. An example is the SU(4) R-symmetry of N=4 D=4 NCSYM. The gauge fields, along with all closed string bulk modes, are not on-shell external states but do appear as off-shell intermediate states in non-planar processes; these closed string modes are thereby holographically encoded in the NCFT.

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arXiv2000

Comments on Unstable Branes

We argue that type II string theories contain unstable NS4 branes, which descend from a conjectured unstable M4 brane of M-theory. Assuming that an M2 brane can arise in M5 brane/anti-brane annihilation, the unstable M4 brane, and also an unstable M3 brane, must exist as sphalerons. We compare the tensions of the unstable NS4 branes, M4 brane, and related type II unstable D-branes, and present 11d supergravity solutions for unstable Mp branes for all p. We study the Z_2 gauge symmetry on the worldvolume of unstable branes, and argue that it can never be unbroken in the presence of lower brane charge.

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arXiv2000

On Inherited Duality in N=1 d=4 Supersymmetric Gauge Theories

Four-dimensional N=1 supersymmetric gauge theories with two adjoints and a quartic superpotential are believed, from AdS/CFT duality, to have SL(2,Z) invariance. In this note we review an old, unpublished argument for this property, based solely on field theory. The technique involves a complexified flavor rotation which deforms an N=2 supersymmetric gauge theory with matter to an N=1 theory, leaving all holomorphic invariants unchanged. We apply this to the N=1 gauge theory with two massless adjoints and show that it has the same auxiliary torus as that of N=4 gauge theory, from which SL(2,Z) invariance follows. In an appendix, we check that our arguments are consistent with earlier work on the SU(2) case. Our technique is general and applies to many other N=1 theories.

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arXiv1994

``Integrating in'' and exact superpotentials in 4d

We discuss integrating out matter fields and integrating in matter fields in four dimensional supersymmetric gauge theories. Highly nontrivial exact superpotentials can be easily obtained by starting from a known theory and integrating in matter.

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arXiv1993

Exact N=2 Landau-Ginzburg Flows

We find exactly solvable N=2-supersymmetric flows whose infrared fixed points are the N=2 minimal models. The exact S-matrices and the Casimir energy (a c-function) are determined along the entire renormalization group trajectory. The c-function runs from c=3 (asymptotically) in the UV to the N=2 minimal model values of the central charge in the IR, leading us to interpret these theories as the Landau-Ginzburg models with superpotential $X^{k+2}$. Consideration of the elliptic genus gives further support for this interpretation. We also find an integrable model in this hierarchy which has spontaneously-broken supersymmetry and superpotential $X$, and a series of integrable models with (0,2) supersymmetry. The flows exhibit interesting behavior in the UV, including a relation to the N=2 super sine-Gordon model. We speculate about the relation between the kinetic term and the cigar target-space metric.

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arXiv1993

Central charges without finite-size effects

We show how to obtain the ultraviolet central charge from the exact S-matrix for a wide variety of models with a $U(1)$ symmetry. This is done by coupling the $U(1)$ current $J$ to a background field. In an $N$=2 superconformal theory with $J$ the fermion number current, the OPE of $J$ with itself and hence the free energy are proportional to $c$. By deforming the supersymmetry into affine $\widehat SU(2)_q$ quantum-group symmetry, this result can be generalized to many $U(1)$-invariant theories, including the N=0 and N=1 sine-Gordon models and the $SU(2)_k$ WZW models. This provides a consistency check on a conjectured S-matrix completely independent of the finite-size effects expressed in terms of dilogarithms resulting from the thermodynamic Bethe ansatz.

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arXiv1992

A New Supersymmetric Index

We show that ${\rm Tr}(-1)^F F e^{-βH}$ is an index for $N$=2 supersymmetric theories in two dimensions, in the sense that it is independent of almost all deformations of the theory. This index is related to the geometry of the vacua (Berry's curvature) and satisfies an exact differential equation as a function of $β$. For integrable theories we can also compute the index thermodynamically, using the exact $S$-matrix. The equivalence of these two results implies a highly non-trivial equivalence of a set of coupled integral equations with these differential equations, among them Painleve III and the affine Toda equations.

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