arXiv subjects

I. N. McArthur

Publications and source records attributed to I. N. McArthur.

At least 19 recordsLinked to original sources

arXiv2023

A supersymmetric nonlinear sigma model analogue of the ModMax theory

A decade ago, it was shown that associated with any model for $\mathsf{U}(1)$ duality-invariant nonlinear electrodynamics there is a unique $\mathsf{U}(1)$ duality-invariant supersymmetric nonlinear sigma model formulated in terms of chiral and complex linear superfields. Here we study the ${\cal N}=1$ superconformal $σ$-model analogue of the conformal duality-invariant electrodynamics known as the ModMax theory. We derive its dual formulation in terms of chiral superfields and show that the target space is a Kähler cone with $\mathsf{U}(1)\times \mathsf{U}(1)$ being the connected component of the isometry group.

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arXiv2023

Self-dual supersymmetric nonlinear sigma models

In four-dimensional N=1 Minkowski superspace, general nonlinear sigma models with four-dimensional target spaces may be realised in term of CCL (chiral and complex linear) dynamical variables which consist of a chiral scalar, a complex linear scalar and their conjugate superfields. Here we introduce CCL sigma models that are invariant under U(1) "duality rotations" exchanging the dynamical variables and their equations of motion. The Lagrangians of such sigma models prove to obey a partial differential equation that is analogous to the self-duality equation obeyed by U(1) duality invariant models for nonlinear electrodynamics. These sigma models are self-dual under a Legendre transformation that simultaneously dualises (i) the chiral multiplet into a complex linear one; and (ii) the complex linear multiplet into a chiral one. Any CCL sigma model possesses a dual formulation given in terms of two chiral multiplets. The U(1) duality invariance of the CCL sigma model proves to be equivalent, in the dual chiral formulation, to a manifest U(1) invariance rotating the two chiral scalars. Since the target space has a holomorphic Killing vector, the sigma model possesses a third formulation realised in terms of a chiral multiplet and a tensor multiplet. The family of U(1) duality invariant CCL sigma models includes a subset of N=2 supersymmetric theories. Their target spaces are hyper Kahler manifolds with a non-zero Killing vector field. In the case that the Killing vector field is triholomorphic, the sigma model admits a dual formulation in terms of a self-interacting off-shell N=2 tensor multiplet. We also identify a subset of CCL sigma models which are in a one-to-one correspondence with the U(1) duality invariant models for nonlinear electrodynamics. The target space isometry group for these sigma models contains a subgroup U(1) x U(1).

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arXiv2018

Deriving all p-brane superalgebras via integrability

In previous work we demonstrated that the enlarged super-Poincare algebras which underlie p-brane and D-brane actions in superstring theory can be directly determined based on the integrability of supersymmetry transformations assigned to fields appearing in Wess-Zumino terms. In that work we derived p-brane superalgebras for p = 2 and 3. Here we extend our previous results and give a compact expression for superalgebras for all valid p.

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arXiv2017

p-brane superalgebras via integrability

It has long been appreciated that superalgebras with bosonic and fermionic generators additional to those in the super-Poincare algebra underlie p-brane and D-brane actions in superstring theory. These algebras have been revealed via "bottom up" approaches, involving consideration of Noether charges, and by "top down" approaches, involving the construction of manifestly supersymmetry invariant Wess-Zumino actions. In this paper, we give an alternative derivation of these algebras based on integrability of supersymmetry transformations assigned to fields in order to solve a cohomology problem related to the construction of Wess-Zumino terms for p-brane and D-brane actions.

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arXiv2015

Coset construction of a D-brane gauge field

D-branes have a world-volume U(1) gauge field A whose field strength F = dA gives rise to a Born-Infeld term in the D-brane action. Supersymmetry and kappa symmetry transformations of A are traditionally inferred by the requirement that the Born-Infeld term is consistent with both supersymmetry and kappa symmetry of the D-brane action. In this paper, we show that integrability of the assigned supersymmetry transformations leads to a extension of the standard supersymmetry algebra that includes a fermionic central charge. We construct a superspace one-form on an enlarged superspace related by a coset construction to this centrally extended algebra whose supersymmetry and kappa symmetry transformations are derived, rather than inferred. It is shown that under pullback, these transformations are of the form expected for the D-brane U(1) gauge field. We relate these results to manifestly supersymmetric approaches to construction of D-brane actions.

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arXiv2013

Goldstino superfields in AdS_4

Spontaneous breaking of global supersymmetries results in Goldstino fields which provide a nonlinear realisation of the supersymmetry algebra. A finite supersymmetry transformation of a Goldstino field can be used to generate a superfield whose components provide a linear realisation of the supersymmetry algebra. This construction also automatically determines the action of the algebra of supercovariant derivatives on Goldstino superfields, essential to the efficient computation of manifestly supersymmetric component actions for the Goldstinos, including coupling to matter fields. In this paper, we extend known constructions of Goldstino superfields resulting from spontaneous breaking of supersymmetry in flat four-dimensional N =1 superspace to spontaneous breaking of N =1 and N =2 supersymmetry in AdS_4.

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arXiv2011

Goldstino superfields for spontaneously broken N=2 supersymmetry

We examine spontaneously broken N=2 supersymmetry in four dimensions and associate a spinor superfield with each Goldstino via a finite supersymmetry transformation with parameters that are the Grassmann coordinates of N=2 superspace. Making use of a special choice of coset parametrization allows us to develop a version of nonlinearly realized N=2 supersymmetry for which the associated Goldstino superfields are defined on harmonic superspace, thereby providing a natural mechanism for construction of a Goldstino action. The corresponding superfield Lagrangian is an O(4) multiplet. This property is used to reformulate the Goldstino action in projective superspace and in conventional N=2 superspace. We show how to generate matter couplings of the Goldstinos to supersymmetric matter using the N=2 harmonic, projective and full superspaces. As a bi-product of our consideration, we also derive an N=2 chiral Goldstino action.

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arXiv2010

Nonlinear realizations of symmetries and unphysical Goldstone bosons

The embedding of a $p$-brane into higher dimensional spacetime breaks not only translational symmetries transverse to the worldvolume, but also Lorentz symmetries. There exist formulations for $p$-brane actions which associate Goldstone bosons with the generators of the broken Lorentz symmetries. These Goldstone bosons are unphysical, in that they can be eliminated in favour of other Goldstone bosons either via their equations of motion or via the imposition of an inverse Higgs constraint. In this paper, we examine the inter-relationship between the coset parameterization necessary to implement the inverse Higgs constraint, the equivalence of the inverse Higgs constraint to equations of motion, and the ability to find versions of the action with no explicit dependence on the unphysical Goldstone bosons. This is evidence that the unphysical Goldstone bosons are gauge degrees of freedom associated with an enlarged isotropy group. In addition to $p$-brane actions, a number of other cases, including conformally invariant dilaton actions, are shown to exhibit the same structure.

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arXiv2006

On the two-loop four-derivative quantum corrections in 4D N = 2 superconformal field theories

In \cN = 2, 4 superconformal field theories in four space-time dimensions, the quantum corrections with four derivatives are believed to be severely constrained by non-renormalization theorems. The strongest of these is the conjecture formulated by Dine and Seiberg in hep-th/9705057 that such terms are generated only at one loop. In this note, using the background field formulation in \cN = 1 superspace, we test the Dine-Seiberg proposal by comparing the two-loop F^4 quantum corrections in two different superconformal theories with the same gauge group SU(N): (i) \cN = 4 SYM (i.e. \cN = 2 SYM with a single adjoint hypermultiplet); (ii) \cN = 2 SYM with 2N hypermultiplets in the fundamental. According to the Dine-Seiberg conjecture, these theories should yield identical two-loop F^4 contributions from all the supergraphs involving quantum hypermultiplets, since the pure \cN = 2 SYM and ghost sectors are identical provided the same gauge conditions are chosen. We explicitly evaluate the relevant two-loop supergraphs and observe that the F^4 corrections generated have different large N behaviour in the two theories under consideration. Our results are in conflict with the Dine-Seiberg conjecture.

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arXiv2006

Low-energy dynamics in N = 2 super QED: Two-loop approximation

The two-loop (Euler-Heisenberg-type) effective action for N = 2 supersymmetric QED is computed using the N = 1 superspace formulation. The effective action is expressed as a series in supersymmetric extensions of F^{2n}, where n=2,3,..., with F the field strength. The corresponding coefficients are given by triple proper-time integrals which are evaluated exactly. As a by-product, we demonstrate the appearance of a non-vanishing F^4 quantum correction at the two-loop order. The latter result is in conflict with the conclusion of hep-th/9710142 that no such quantum corrections are generated at two loops in generic N = 2 SYM theories on the Coulomb branch. We explain a subtle loophole in the relevant consideration of hep-th/9710142 and re-derive the F^4 term from harmonic supergraphs.

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arXiv2005

The SU(N) Matrix Model at Two Loops

Multi-loop calculations of the effective action for the matrix model are important for carrying out tests of the conjectured relationship of the matrix model to the low energy description of M-theory. In particular, comparison with N-graviton scattering amplitudes in eleven-dimensional supergravity requires the calculation of the effective action for the matrix model with gauge group SU(N). A framework for carrying out such calculations at two loops is established in this paper. The two-loop effective action is explicitly computed for a background corresponding to the scattering of a single D0-brane from a stack of N-1 D0-branes, and the results are shown to agree with known results in the case N=2.

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arXiv2004

Relaxed super self-duality and N = 4 SYM at two loops

A closed-form expression is obtained for a holomorphic sector of the two-loop low-energy effective action for the N = 4 super Yang-Mills theory on its Coulomb branch where the gauge group SU(N) is spontaneously broken to SU(N-1) x U(1) and the dynamics is described by a single Abelian N = 2 vector multiplet. In the framework of the background-field method, this holomorphic sector is singled out by computing the effective action for a background N = 2 vector multiplet satisfying a relaxed super self-duality condition. At the two-loop level, the N = 4 SYM effective action is shown to possess no F^4 term (with F the U(1) field strength), in accordance with the Dine-Seiberg non-renormalization conjecture hep-th/9705057 and its generalized form given in hep-th/0310025. An unexpected outcome of our calculation is that no (manifestly supersymmetric invariant generating) F^6 quantum correction occurs at two loops. This is in conflict with previous results.

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arXiv2004

Relaxed super self-duality and effective action

A closed-form expression is obtained for a holomorphic sector of the two-loop Euler-Heisenberg type effective action for N = 2 supersymmetric QED derived in hep-th/0308136. In the framework of the background-field method, this sector is singled out by computing the effective action for a background N = 2 vector multiplet satisfying a relaxed super self-duality condition. The approach advocated in this letter can be applied, in particular, to the study of the N = 4 super Yang-Mills theory on its Coulomb branch.

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arXiv2003

On the Background Field Method Beyond One Loop: A manifestly covariant derivative expansion in super Yang-Mills theories

There are currently many string inspired conjectures about the structure of the low-energy effective action for super Yang-Mills theories which require explicit multi-loop calculations. In this paper, we develop a manifestly covariant derivative expansion of superspace heat kernels and present a scheme to evaluate multi-loop contributions to the effective action in the framework of the background field method. The crucial ingredient of the construction is a detailed analysis of the properties of the parallel displacement propagators associated with Yang-Mills supermultiples in N-extended superspace.

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arXiv2002

Low energy dynamics from deformed conformal symmetry in quantum 4D N = 2 SCFTs

We determine the one-loop deformation of the conformal symmetry of a general N}=2 superconformally invariant Yang-Mills theory. The deformation is computed for several explicit examples which have a realization as world-volume theories on a stack of D3 branes. These include (i) N=4 SYM with gauge groups SU(N), USp(2N) and SO(N); (ii) USp(2N) gauge theory with one hypermultiplet in the traceless antisymmetric representation and four hypermultiplets in the fundamental; (iii) quiver gauge theory with gauge group SU(N)xSU(N) and two hypermultiplets in the bifundamental representations (N,\bar N) and (bar N,N). The existence of quantum corrections to the conformal transformations imposes restrictions on the effective action which we study on a subset of the Coulomb branch corresponding to the separation of one brane from the stack. In the N=4 case, the one-loop corrected transformations provide a realization of the conformal algebra; this deformation is shown to be one-loop exact. For the other two models, higher-loop corrections are necessary to close the algebra. Requiring closure, we infer the two-loop conformal deformation.

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arXiv2002

On quantum deformation of conformal symmetry: Gauge dependence via field redefinitions

The effective action in gauge theories is known to depend on a choice of gauge fixing conditions. This dependence is such that any change of gauge conditions is equivalent to a field redefinition in the effective action. In this sense, the quantum deformation of conformal symmetry in the N = 4 super Yang-Mills theory, which was computed in 't Hooft gauge in hep-th/9808039 and hep-th/0203236, is gauge dependent. The deformation is an intrinsic property of the theory in that it cannot be eliminated by a local choice of gauge (although we sketch a field redefinition induced by a nonlocal gauge which, on the Coulomb branch of the theory, converts the one-loop quantum-corrected conformal transformations to the classical ones). We explicitly compute the deformed conformal symmetry in R_ξgauge. The conformal transformation law of the gauge field turns out to be ξ-independent. We construct the scalar field redefinition which relates the 't Hooft and R_ξgauge results. A unique feature of 't Hooft gauge is that it makes it possible to consistently truncate the one-loop conformal deformation to the terms of first order in derivatives of the fields such that the corresponding transformations form a field realization of the conformal algebra.

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arXiv2002

Quantum metamorphosis of conformal symmetry in N = 4 super Yang-Mills theory

In gauge theories, not all rigid symmetries of the classical action can be maintained manifestly in the quantization procedure, even in the absence of anomalies. If this occurs for an anomaly-free symmetry, the effective action is invariant under a transformation that differs from its classical counterpart by quantum corrections. As shown by Fradkin and Palchik years ago, such a phenomenon occurs for conformal symmetry in quantum Yang-Mills theories with vanishing beta function, such as the N = 4 super Yang-Mills theory. More recently, Jevicki et al demonstrated that the quantum metamorphosis of conformal symmetry sheds light on the nature of the AdS/CFT correspondence. In this paper, we derive the conformal Ward identity for the bosonic sector of the N = 4 super Yang-Mills theory using the background field method. We then compute the leading quantum modification of the conformal transformation for a specific Abelian background which is of interest in the context of the AdS/CFT correspondence. In the case of scalar fields, our final result agrees with that of Jevicki et al. The resulting vector and scalar transformations coincide with those which are characteristic of a D3-brane embedded in AdS5 x S5.

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arXiv2001

Goldstone multiplet for partially broken superconformal symmetry

The bosonic parts of D3-brane actions in AdS(5) backgrounds are known to have symmetries which are field-dependent extensions of conformal transformations of the worldvolume coordinates. Using the coset space SU(2,2|1)/SO(4,1), we apply the method of nonlinear realizations to construct a four-dimensional N = 1 off-shell supersymmetric action which has a generalized field-dependent superconformal invariance. The Goldstone fields for broken scale, chiral and S-supersymmetry transformations form a chiral supermultiplet.

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