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Theta, time reversal and temperature

SU(N ) gauge theory is time reversal invariant at θ = 0 and θ = π. We show that at θ = π there is a discrete ’t Hooft anomaly involving time reversal and the center symmetry. This anomaly leads to constraints on the vacua of the theory. It follows that at θ = π the vacuum cannot be a trivial non-degenerate gapped state. (By contrast, the vacuum at θ = 0 is gapped, non-degenerate, ...

Shortening anomalies in supersymmetric theories

We present new anomalies in two-dimensional \( \mathcal{N}=\left(2,2\right) \) superconformal theories. They obstruct the shortening conditions of chiral and twisted chiral multiplets at coincident points. This implies that marginal couplings cannot be promoted to background superfields in short representations. Therefore, standard results that follow from \( ...

Correlation functions of Coulomb branch operators

We consider the correlation functions of Coulomb branch operators in four-dimensional \( \mathcal{N} \) = 2 Superconformal Field Theories (SCFTs) involving exactly one antichiral operator. These extremal correlators are the “minimal” non-holomorphic local observables in the theory. We show that they can be expressed in terms of certain determinants of derivatives of the four-sphere ...

Disorder in large-N theories

We consider Euclidean Conformal Field Theories perturbed by quenched disorder, namely by random fluctuations in their couplings. Such theories are relevant for second-order phase transitions in the presence of impurities or other forms of disorder. Theories with quenched disorder often flow to new fixed points of the renormalization group. We begin with disorder in free field ...

Is the relaxion an axion?

We consider the recently proposed cosmological relaxation mechanism where the hierarchy problem is ameliorated, and the electroweak (EW) scale is dynamically selected by a slowly rolling axion field. We argue that, in its simplest form, the construction breaks a gauge symmetry that always exists for pseudo-Nambu-Goldstone bosons (in particular the axion). The small parameter in the ...

Cardy formulae for SUSY theories in d = 4 and d = 6

without supersymmetry, JHEP 10 Lorenzo Di Pietro and Zohar Komargodski One can count BPS representations weighted by (1)F , or, equivalently, study supersymmetric partition functions by compactifying the

On scale and conformal invariance in four dimensions

We study the implications of scale invariance in four-dimensional quantum field theories. Imposing unitarity, we find that infinitely many matrix elements vanish in a suitable kinematical configuration. This vanishing is a nontrivial necessary condition for conformality. We provide an argument why this is expected to be a sufficient condition as well, thereby linking scale and ...

Anomalies, conformal manifolds, and spheres

The two-point function of exactly marginal operators leads to a universal contribution to the trace anomaly in even dimensions. We study aspects of this trace anomaly, emphasizing its interpretation as a sigma model, whose target space \( \mathrm{\mathcal{M}} \) is the space of conformal field theories (a.k.a. the conformal manifold). When the underlying quantum field theory is ...

Scale invariance, conformality, and generalized free fields

This paper addresses the question of whether there are 4D Lorentz invariant unitary quantum field theories with scale invariance but not conformal invariance. An important loophole in the arguments of Luty-Polchinski-Rattazzi and Dymarsky-Komargodski-Schwimmer-Theisen is that trace of the energy-momentum tensor T could be a generalized free field. In this paper we rule out this ...

Sphere partition functions and the Zamolodchikov metric

We study the finite part of the sphere partition function of d-dimensional Conformal Field Theories (CFTs) as a function of exactly marginal couplings. In odd dimensions, this quantity is physical and independent of the exactly marginal couplings. In even dimensions, this object is generally regularization scheme dependent and thus unphysical. However, in the presence of additional ...

(Non-)decoupled supersymmetric field theories

We study some consequences of coupling supersymmetric theories to (super)gravity. To linear order, the couplings are determined by the energy-momentum supermultiplet. At higher orders, the couplings are determined by contact terms in correlation functions of the energy-momentum supermultiplet. We focus on the couplings of one particular field in the supergravity multiplet, the ...

The Casimir energy in curved space and its supersymmetric counterpart

We study d-dimensional Conformal Field Theories (CFTs) on the cylinder, \( {S}^{d-1}\times \mathrm{\mathbb{R}} \), and its deformations. In d = 2 the Casimir energy (i.e. the vacuum energy) is universal and is related to the central charge c. In d = 4 the vacuum energy depends on the regularization scheme and has no intrinsic value. We show that this property extends to ...

The geometry of supersymmetric partition functions

We consider supersymmetric field theories on compact manifolds \( \mathcal{M} \) and obtain constraints on the parameter dependence of their partition functions \( {Z_{\mathcal{M}}} \). Our primary focus is the dependence of \( {Z_{\mathcal{M}}} \) on the geometry of \( \mathcal{M} \), as well as background gauge fields that couple to continuous flavor symmetries. For \( ...

Soft terms from broken symmetries

Matthew Buican 1 Zohar Komargodski 0 0 School of Natural Sciences, Institute for Advanced Study , Princeton, NJ 08540, U.S.A 1 Department of Physics, CERN Theory Division , CH-1211, Geneva 23

A bound on the superpotential

We prove a general bound on the superpotential in theories with broken supersymmetry and broken R-symmetry, |〈W〉| \( \frac{1}{2} \) f a F, where f a and F are the R-axion and Goldstino decay constants, respectively. The bound holds for weakly coupled as well as strongly coupled theories, thereby providing an exact result in theories with broken supersymmetry. We briefly discuss ...