We classify a one-parameter family,   <math> <mtext>confcar</mtext> <msub> <mi>r</mi> <mi>z</mi> </msub> <mfenced> <mrow> <mi>d</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfenced> </math>  $$ \mathfrak{confcar}{\mathfrak{r}}_z\left(d+1\right) $$ , of conformal extensions of the Carroll algebra in arbitrary dimension with z being the anisotropic scaling exponent. We further obtain their infinite-dimensional extensions,   <math> <msub> <mover> <mtext>confcarr</mtext> <mo>~</mo> </mover> <mi>z</mi> </msub> <mfenced> <mrow> <mi>d</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfenced> </math>  $$ {\overset{\sim }{\mathfrak{confcarr}}}_z\left(d+1\right) $$ , and discuss their corresponding finite-dimensional truncated subalgebras when the scaling exponent is integer or half-integer. For all these conformal extensions, we also constrain the 2-point and 3-point correlation functions with electric and/or magnetic features.

Iran

Hamid Afshar

France

Xavier Bekaert

Mojtaba Najafizadeh

Classification of conformal carroll algebras

The exploration of scalar field theories that exhibit Carroll and Galilei symmetries has attracted a lot of attention. In this paper, we generalize these studies to fermionic field theories and construct consistent electric and magnetic descriptions of Carrollian and Galilean spin <math><mfrac><mn>1</mn><mn>2</mn></mfrac></math> fermions. We showcase various methods that offer complementary perspectives into the limiting process of the underlying relativistic theories. Moreover, we extend our study to <math><mi>N</mi><mo>=</mo><mn>1</mn></math> off-shell supersymmetric field theories in four dimensions. By introducing suitable Grassmann-analyticity conditions, we formulate the corresponding super Carrollian and super-Galilean theories. These theories combine the established Carroll/Galilei scalars with the Carroll/Galilei fermions and a range of auxiliary fields into supermultiplets.

United States

Konstantinos Koutrolikos

Super-Carrollian and super-Galilean field theories

The invariance of physical observables like particle’s mass under a local field redefinition is a well-known and important property of quantum field theory. In this paper, on the other hand, we investigate nonlocal field redefinitions eliminating a physical observable from a theory. Indeed, by giving explicit examples, we present invertible nonlocal field redefinitions reducing a massive theory to the massless one, and vice versa. The studied examples are: classical harmonic oscillator, the scalar field theory, and the Dirac field theory.

Massive to massless by applying a nonlocal field redefinition

We construct, for the first time, an off-shell supersymmetric continuous spin gauge theory in 4-dimensional Minkowski spacetime, in both constrained and unconstrained Lagrangian formulations. As an extension to the on-shell description [1], we employ an auxiliary field to close the algebra of supersymmetry transformations off-shell. The 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 massless continuous spin supermultiplet is then denoted by (Φ, H; Ψ), comprised of a dynamical and a non-dynamical complex scalar continuous spin gauge fields Φ and H, as well as a Dirac continuous spin gauge field Ψ. In particular, we demonstrate that the off-shell continuous spin supermultiplet, in a limit, reproduces off-shell supersymmetry transformations of the known scalar supermultiplet (0, 1/2), all integer-spin supermultiplets (s, s + 1/2), s ≥ 1, and all half-integer spin supermultiplets (s − 1/2, s), s ≥ 1.

Off-shell supersymmetric continuous spin gauge theory

We consider unconstrained formulation of the higher spin gauge theory in anti–de Sitter (AdS) spacetime, given by actions [A. Y. Segal, arXiv:0103028; M. Najafizadeh, Phys. Rev. D 98, 125012 (2018)], and provide on-shell supersymmetry transformations for the <math><mi>N</mi><mo>=</mo><mn>1</mn></math> unconstrained massless higher spin supermultiplet in four-dimensional <math><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math>. Such an irreducible supermultiplet <math><mo>(</mo><msub><mi>Φ</mi><mn>1</mn></msub><mo>,</mo><msub><mi>Φ</mi><mn>2</mn></msub><mo>;</mo><msub><mi>Ψ</mi><mn>1</mn></msub><mo>,</mo><msub><mi>Ψ</mi><mn>2</mn></msub><mo>)</mo></math> contains a pair of bosonic fields, with opposite parity, which are generating functions (infinite collection of totally symmetric real tensor fields of all integer rank <math><mi>s</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>∞</mi></math>), as well as two fermionic fields, which have opposite signs of the AdS radius, that are spinorial generating functions (infinite tower of totally symmetric Majorana spinor-tensor fields of all half-integer spin <math><mi>s</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>,</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>,</mo><mo>…</mo><mo>,</mo><mi>∞</mi></math>).

Unconstrained massless higher spin supermultiplet in <math><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math> spacetime

Taking into account the Schuster-Toro action and its fermionic analogue discovered by us, we supersymmetrize unconstrained formulation of the continuous spin gauge field theory. Afterwards, building on the Metsaev actions, we supersymmetrize constrained formulation of the theory. In each formulation, we provide supersymmetry transformations for the   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 supermultiplet in four-dimensional flat space-time, in which continuous spin particle (CSP) is considered to be a complex scalar continuous spin field, and its super- partner which can be called “ CSPino ” is considered to be a Dirac continuous spin field. It is shown that the algebra of these supersymmetry transformations are closed on-shell. Furthermore, we investigate whether obtained supersymmetry transformations reproduce the known result of the higher spin gauge field theory in the helicity limit. Finally, we illustrate how these two separate set of obtained transformations are related to each other.

Supersymmetric continuous spin gauge theory

Building on Segal’s local free action principle for bosonic unconstrained higher spin gauge fields in <math><mi>d</mi></math>-dimensional <math><mrow><mo>(</mo><mi>A</mi><mo>)</mo><mi>d</mi><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow></mrow></math> spacetime, we present a similar action principle à la Segal for fermions in <math><mi>d</mi></math>-dimensional <math><mrow><mo>(</mo><mi>A</mi><mo>)</mo><mi>d</mi><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow></mrow></math> spacetime. Moreover, at the level of equations of motion, we demonstrate how the Fronsdal and the Fang-Fronsdal equations in <math><mi>d</mi></math>-dimensional <math><mrow><mo>(</mo><mi>A</mi><mo>)</mo><mi>d</mi><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow></mrow></math> spacetime are related, respectively, to the Euler-Lagrange equations of the bosonic and fermionic higher spin actions mentioned above.

Local action for fermionic unconstrained higher spin gauge fields in AdS and dS spacetimes

In this paper, we first propose the bosonic (fermionic) modified Wigner equations for continuous spin particle (CSP). Secondly, starting from the (Fang-)Fronsdal-like equation, we will reach to the modified action of bosonic (fermionic) continuous spin gauge field in flat spacetime, presented recently by Metsaev in (A)dS spacetime. We shall also explain how to obtain the proposed modified Wigner equations from the gauge-fixed equations of motion. Finally, we will consider the massive bosonic (fermionic) higher-spin action and, by taking the infinite spin limit, we will arrive at the modified bosonic (fermionic) CSP action.

Modified Wigner equations and continuous spin gauge field

Action principles for the single and double valued continuous-spin representations of the Poincaré group have been recently proposed in a Segal-like formulation. We address three related issues: first, we explain how to obtain these actions directly from the Fronsdal-like and Fang-Fronsdal-like equations by solving the traceless constraints in Fourier space. Second, we introduce a current, similar to the one of Berends, Burgers and Van Dam, which is bilinear in a pair of scalar matter fields, to which the bosonic continuous-spin field can couple minimally. Third, we investigate the current exchange mediated by a continuous-spin particle obtained from this action principle and investigate whether it propagates the right degrees of freedom, and whether it reproduces the known result for massless higher-spin fields in the helicity limit.