The ultra-violet question in maximally supersymmetric field theories (original) (raw)

Supersymmetry counterterms revisited

Physics Letters B, 2003

Superspace power-counting rules give estimates for the loop order at which divergences can first appear in non-renormalisable supersymmetric field theories. In some cases these estimates can be improved if harmonic superspace, rather than ordinary superspace, is used. The new estimates are in agreement with recent results derived from unitarity calculations for maximally supersymmetric Yang-Mills theories in five and six dimensions. For N = 8 supergravity in four dimensions, we speculate that the onset of divergences may correspondingly occur at the six loop order.

Revisiting supergravity and super Yang-Mills renormalization

AIP Conference Proceedings, 2001

Standard superspace Feynman diagram rules give one estimate of the onset of ultraviolet divergences in supergravity and super Yang-Mills theories. Newer techniques motivated by string theory but which also make essential use of unitarity cutting rules give another in certain cases. We trace the difference to the treatment of higher-dimensional gauge invariance in supersymmetric theories that can be dimensionally oxidized to pure supersymmetric gauge theories.

A note on the UV behaviour of maximally supersymmetric Yang–Mills theories

Physics Letters B, 2009

The question of whether BPS invariants are protected in maximally supersymmetric Yang-Mills theories is investigated from the point of view of algebraic renormalisation theory. The protected invariants are those whose cohomology type differs from that of the action. It is confirmed that one-half BPS invariants (F 4) are indeed protected while the double-trace one-quarter BPS invariant (d 2 F 4) is not protected at two loops in D = 7, but is protected at three loops in D = 6 in agreement with recent calculations. Non-BPS invariants, i.e. full superspace integrals, are also shown to be unprotected.

Ultraviolet divergences in higher dimensional supersymmetric Yang-Mills theories

Physics Letters B, 1984

We determine the loop orders for the onset of allowed ultraviolet divergences in higher dimensional supersymmetrie Yang-Mills theories. Cancellations are controlled by the non-renormalization theorems for the linearly realizable supersymmetries and by the requirement that counterterms display the full non-linear supersymmetries when the classical equations of motion are imposed. The first allowed divergences in the maximal super Yang-Mills theories occur at four loops in five dimensions, three loops in six dimensions and two loops in seven dimensions.

Miraculous ultraviolet cancellations in supersymmetry made manifest

Nuclear Physics B, 1984

We develop the formalism for quantization with manifest linearly realized extended supersymmetry. Together with the use of the background field method, this gives rise to a general non-renormalization theorem that explains all of the "miraculous" cancellations observed to date in supersymmetric field theories and shows in which cases they will be continued to all orders of perturbation theory. In particular, we present the details of N = 2 superfield perturbation theory and show that in renormalizable models in four dimensions, the only infinity that can arise is at the one-loop order in the Yang-Mills coupling constant. The finiteness of the N = 4 supersymmetric Yang-Mills theory is a particular consequence of this result.

Quantum Aspects of Gauge Theories, Supersymmetry and Unification PROCEEDINGS

2000

Abstract: According to the AdS/CFT correspondence, the d = 4, N = 4 SU(N) super Yang-Mills theory is dual to the type IIB string theory compactified on AdS5 × S 5. Most of the tests performed so far are confined to the leading order at large N or equivalently string tree-level. To probe the correspondence beyond this leading order and obtain 1 N 2 corrections is difficult since string one-loop computations on an AdS5 × S 5 background generally are beyond feasibility. However, we will show that the chiral SU(4)R anomaly of the super YM theory provides an ideal testing ground to go beyond leading order in N. In this paper, we review and develop further our previous results [1] that the 1/N 2 corrections to the chiral anomaly on the super YM side can be exactly accounted for by the supergravity/string effective action induced at one loop. 1.

Invariants and divergences in half-maximal supergravity theories

Journal of High Energy Physics, 2013

The invariants in half-maximal supergravity theories in D = 4, 5 are discussed in detail up to dimension eight (e.g. R 4). In D = 4, owing to the anomaly in the rigid SL(2, $ \mathbb{R} $ ) duality symmetry, the restrictions on divergences need careful treatment. In pure $ \mathcal{N}=4 $ supergravity, this anomalous symmetry still implies duality invariance of candidate counterterms at three loops. Provided one makes the additional assumption that there exists a full 16-supercharge off-shell formulation of the theory, counterterms at L ≥ 2 loops would also have to be writable as full-superspace integrals. At the three-loop order such a duality-invariant full-superspace integral candidate counterterm exists, but its duality invariance is marginal in the sense that the full-superspace counter-Lagrangian is not itself duality-invariant. We show that such marginal invariants are not allowable as counterterms in a 16-supercharge off-shell formalism. It is not possible to draw the same c...

Superfield covariant analysis of the divergence structure of noncommutative supersymmetric QED4

Physical Review D, 2004

Commutative supersymmetric Yang-Mills is known to be renormalizable for N = 1, 2, while finite for N = 4. However, in the noncommutative version of the model (NCSQED 4 ) the UV/IR mechanism gives rise to infrared divergences which may spoil the perturbative expansion. In this work we pursue the study of the consistency of NCSQED 4 by working systematically within the covariant superfield formulation. In the Landau gauge, it has already been shown for N = 1 that the gauge field two-point function is free of harmful UV/IR infrared singularities, in the one-loop approximation. Here we show that this result holds without restrictions on the number of allowed supersymmetries and for any arbitrary covariant gauge. We also investigate the divergence structure of the gauge field three-point function in the one-loop approximation. It is first proved that the cancellation of the leading UV/IR infrared divergences is a gauge invariant statement. Surprisingly, we have also found that there exist subleading harmful UV/IR infrared singularities whose cancellation only takes place in a particular covariant gauge. Thus, we conclude that these last mentioned singularities are in the gauge sector and, therefore, do not jeopardize the perturbative expansion and/or the renormalization of the theory.

Renormalizability Properties of Supergravity

Physical Review Letters, 1977

, introduced the now ubiquitous 3-loop "R 4 " supersymmetric counterterm, key to the UV finiteness issue in all supergravity theories, particularly the much discussed N = 8 case. It also established the basic pattern for the corresponding 4-point finite corrections in string theory effective actions. We thank J Franklin for producing this arXiv version.