A. Johansen

Non-perturbative formulas for central functions of supersymmetric gauge theories

Abstract For quantum field theories that flow between ultraviolet and infrared fixed points, central functions, defined from two-point correlators of the stress tensor and conserved currents, interpolate between central charges of the UV and IR critical theories. We develop techniques that allow one to calculate the flows of the central charges and that of the Euler trace anomaly coefficient in a general N = 1 supersymmetric gauge theory. Exact, explicit formulas for SU(Nc) gauge theories in the conformal window are given and analysed. The Euler anomaly coefficient always satisfies the inequality aUV − aIR > 0. This is new evidence in strongly coupled theories that this quantity satisfies a four-dimensional analogue of the c-theorem, supporting the idea of irreversibility of the RG flow. Various other implications are discussed.

Positivity constraints on anomalies in supersymmetric gauge theories

The relation between the trace and R-current anomalies in supersymmetric theories implies that the U(1){sub R}F{sup 2}, U(1){sub R}, and U(1){sub R}{sup 3} anomalies which are matched in studies of N=1 Seiberg duality satisfy positivity constraints. Some constraints are rigorous and others conjectured as four-dimensional generalizations of the Zamolodchikov c theorem. These constraints are tested in a large number of N=1 supersymmetric gauge theories in the non-Abelian Coulomb phase, and they are satisfied in all renormalizable models with unique anomaly-free R current, including those with accidental symmetry. Most striking is the fact that the flow of the Euler anomaly coefficient a{sub UV}{minus}a{sub IR} is always positive, as conjectured by Cardy. {copyright} {ital 1998} {ital The American Physical Society}

Large N limit of orbifold field theories

Abstract We consider a certain orbifoldization of the N = 4 field theories that leads to N = 2, 1, 0 field theories in four dimensions. These theories were recently analyzed using the string theory perturbation technique. It was found that in the large N limit all correlation functions of the orbifold theories coincide with those of N = 4, modulo the rescaling of the gauge coupling constant. In this paper we repeat the same analysis using field theoretical language.

Universality of the operator product expansions of SCFT4

Abstract We study the operator product algebra of the supercurrent J α α and Konishi superfield K in four-dimensional supersymmetric gauge theories. The Konishi superfield appears in the JJ OPE and the algebra is characterized by two central charges c and c ′ and an anomalous dimension h for K . In free field (one-loop) approximation, c ∼ 3 N ν + N χ and c ′ ∼ N χ , where N ν and N χ are, respectively, the number of vector and chiral multiplets in the theory. In higher order c , c ′ and h depend on the gauge and Yukawa couplings and we obtain the two-loop contributions by combining earlier work on c with our own calculations of c ′ and h . The major result is that the radiative corrections to the central charges cancel when the one-loop beta-functions vanish, suggesting that c and c ′ are invariant under continuous deformations of superconformal theories. The behavior of c and c ′ along renormalization group flows is studied from the viewpoint of a c -theorem.

A critical behaviour of anomalous currents, electric-magnetic universality and CFT4

Abstract We discuss several aspects of superconformal field theories in four dimensions (CFT 4 ), in the context of electric-magnetic duality. We analyse the behaviour of anomalous currents under RG flow to a conformal fixed point in N = 1, D = 4 supersymmetric gauge theories. We prove that the anomalous dimension of the Konishi current is related to the slope of the beta function at the critical point. We extend the duality map to the (non-chiral) Konishi current. As a byproduct we compute the slope of the beta function in the strong coupling regime. We note that the OPE of T μν with itself does not close, but mixes with a special additional operator Σ which in general is the Konishi current. We discuss the implications of this fact in generic interacting conformal theories. In particular, a SCFT 4 seems to be naturally equipped with a privileged off-critical deformation Σ and this allows us to argue that electric-magnetic duality can be extended to a neighbourhood of the critical point. We also stress that in SCFT 4 there are two central charges, c and c ′, associated with the stress tensor and Σ, respectively; c and c ′ allow us to count both the vector multiplet and the matter multiplet effective degrees of freedom of the theory.

F theory, geometric engineering and N=1 dualities

Abstract We consider geometric engineering of N = 1 supersymmetric QFTs with matter in terms of a local model for compactification of F-theory on Calabi-Yau fourfold. By bringing 3-branes near 7-branes we engineer N = 1 supersymmetric SU(Nc) gauge theory with Nf flavors in the fundamental. We identify the Higgs branch of this system with the instanton moduli space on the compact four-dimensional space of the 7-brane world-volume. Moreover we show that the Euclidean 3-branes wrapped around the compact part of the 7-brane world-volume can generate superpotential for Nf = Nc − 1 as well as lead to quantum corrections to the moduli space for Nf = Nc. Finally we argue that Seibergs duality for N = 1 supersymmetric QCD may be mapped to T-duality exchanging 7-branes with 3-branes.

Colliding singularities in F-theory and phase transitions

Abstract We study F-theory on elliptic Calabi-Yau three-folds near colliding singularities. We demonstrate that resolutions of those singularities generically correspond to transitions to phases characterized by new tensor multiplets and enhanced gauge symmetry. These are governed by the dynamics of tensionless strings. We also find new transition points which are associated with several small instantons simultaneously shrinking to zero size.

A comment on BPS states in F-theory in 8 dimensions

Abstract We study some aspects of enhanced gauge symmetries in F-theory compactified on K3. We find open string configurations connecting various 7-branes which represent stable BPS states. In this approach we recover Dn and En gauge groups previously found from an analysis of singularities of the moduli space of elliptically fibered K3 manifolds as well as examples of non-perturbative realizations of An groups.

F-THEORY AND LINEAR SIGMA MODELS

We present an explicit method for translating between the linear sigma model and the spectral cover description of SU(r) stable bundles over an elliptically fibered Calabi-Yau manifold. We use this to investigate the four-dimensional duality between (0,2) heterotic and F-theory compactifications. We indirectly find that much interesting heterotic information must be contained in the ‘spectral bundle’ and in its dual description as a gauge theory on multiple F-theory 7-branes. A by-product of these efforts is a method for analyzing semistability and the splitting type of vector bundles over an elliptic curve given as the sheaf cohomology of a monad.

ℤ2 as the topological origin of B + L violation in the hot electroweak theory

Abstract The space of static finite-energy configurations in the electroweak theory admits a ℤ 2 2 topological structure. More precisely, we show that this space contains two disconnected sectors of unstable gauge-Higgs fields odd under a properly defined generalized parity. This classification extends the description of baryon- and lepton-number violating electroweak processes to the symmetric phase of the theory. Configurations with odd pure-gauge behaviour at spatial infinity, such as the sphaleron, multisphalerons, as well as an infinite surface of their equivalents, have half-integer Chern—Simons number and mediate B + L violating processes in the early universe. Finite-energy configurations with even pure-gauge behaviour, such as the S * new sphaleron, are topologically equivalent to the vacuum and are irrelevant for B + L violation. Electroweak string configurations comprise continuous families of sphaleron equivalents as well as configurations equivalent to the vacuum. We discuss the possible formation of B + L violating quark-lepton condensates in the symmetric high-temperature phase of the electroweak theory.