We present a nongeometric derivation of <math><mi>N</mi><mo>=</mo><mn>1</mn></math> Super Yang-Mills by focusing on the consistency of interactions that extend the free vector supermultiplet rather than assuming gauge invariance under extended symmetries. By utilizing a superspace first-order description, the theory is given in closed form as a third-order polynomial, which includes a single cubic interaction term instead of an infinite series, thus eliminating the need for a special gauge. The geometrical interpretation of the theory emerges, as opposed to being presupposed.

United States

Konstantinos Koutrolikos

Just another field theory approach to <math><mi>N</mi><mo>=</mo><mn>1</mn></math> super-Yang-Mills theory and the origin of intrinsic supergeometry

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.

Iran

Mojtaba Najafizadeh

Super-Carrollian and super-Galilean field theories

We investigate the contribution of higher spin particles in the signal of direct detection searches for dark matter. We consider a bosonic or fermionic higher spin dark matter (HSDM) candidate which interacts with the Standard Model via a dark U(1) mediator. For a particular subclass of interactions, spin-polarized targets may be used for spin determination: The angular dependence of scatterings can distinguish integer (spin-s) vs. half-integer (spin-<math><mi>s</mi><mo>+</mo><mn>1</mn><mo>/</mo><mn>2</mn></math>), while the recoil energy dependence of the signal determines s. We consider also the signal of a supersymmetric higher spin dark sector, which suggests a characteristic signal (“SUSY Rilles”) for directional direct detection.

Leah Jenks

Canada

Evan McDonough

Stephon Alexander

S. James Gates

Towards a direct detection of the spin of dark matter

Dp-branes acquire effective nonlinear descriptions whose bosonic part is related to the Born-Infeld action. This nonlinearity has been proven to be a consequence of the partial <math><mi>N</mi><mo>=</mo><mn>2</mn><mo>→</mo><mi>N</mi><mo>=</mo><mn>1</mn></math> supersymmetry breaking, originating from the solitonic nature of the branes. In this work, we focus on the effective descriptions of D2-branes. Using the Goldstone multiplet interpretation of the action and the method of nilpotent <math><mi>N</mi><mo>=</mo><mn>2</mn></math> superfields, we construct the 3D, <math><mi>N</mi><mo>=</mo><mn>1</mn></math> superspace effective action which makes the first supersymmetry manifest and realizes the second, spontaneously broken, supersymmetry nonlinearly. We show that there are two such supersymmetric extensions of the 3D Born-Infeld action which correspond to the dynamics of the 3D Maxwell-Goldstone multiplet and the 3D projection of the Tensor-Goldstone multiplet respectively. Moreover, we demonstrate that these results are derived by applying the constrained superfield approach on the <math><mi>N</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>D</mi><mo>=</mo><mn>3</mn></math> vector and chiral multiplets after expanding them around a nontrivial vacuum. We find that these two descriptions are related by a duality transformation which results in the inversion of a dimensionless parameter. For both descriptions we derive the explicit bosonic and fermionic parts of the 3D super Born-Infeld action. Finally, consider the deformation of the Maxwell-Goldstone superspace action by the characteristic Chern-Simons-like, gauge invariant, mass term.

Yangrui Hu

Nonlinear supersymmetry and 3D supersymmetric Born-Infeld theory

A new description of free massless superfields of arbitrary superspin <math><mi>Y</mi></math> (<math><mi>Y</mi><mo>&gt;</mo><mn>1</mn><mo>/</mo><mn>2</mn></math>) is proposed. Following the first-order philosophy, we relax some of the properties (reality, gauge redundancy) of the unconstrained higher spin prepotentials and we construct first and half order invariants quantities. These are used to write trivially invariant actions. Additional auxiliary superfields that play the role of spin connections are used to enforce a new local symmetry that restores the degrees of freedom.

Superspace first-order formalism for massless arbitrary superspin supermultiplets

An explicit form for the Lagrangian of a massive arbitrary half-integer super-spin Y = s + 1/2 supermultiplet is obtained in 4D,   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 superspace. This is accomplished by the introduction of a tower of pairs of auxiliary superfields of increasing rank which are required to vanish on-shell for free theories. In the massless limit almost all auxiliary super- fields decouple except one, which plays the role of compensator as required by the emergent gauge redundancy of the Lagrangian description of the massless theory. The number of off-shell degrees of freedom carried by the theory is   <math> <mfrac> <mn>8</mn> <mn>3</mn> </mfrac> </math>  $$ \frac{8}{3} $$  (s + 1)(4s 2 + 11s + 3). For s = 1 our results are in agreement with those obtained in [1].

Superspace formulation of massive half-integer superspin

We give an explicit superspace construction of higher spin conserved supercurrents built out of 4D,  <math><mi>N</mi><mo>=</mo><mn>1</mn></math> $$ \mathcal{N}=1 $$ massless supermultiplets of arbitrary spin. These supercurrents are gauge invariant and generate a large class of cubic interactions between a massless supermultiplet with superspin Y 1 = s 1 + 1/2 and two massless supermultiplets of arbitrary superspin Y 2. These interactions are possible only for s 1 ≥ 2Y 2. At the equality, the supercurrent acquires its simplest form and defines the supersymmetric, higher spin extension of the linearized Bel-Robinson tensor.

Brazil

Russia

I. Buchbinder

S. Gates

Czechia

Conserved higher spin supercurrents for arbitrary spin massless supermultiplets and higher spin superfield cubic interactions

We consider a four dimensional generalized Wess-Zumino model formulated in terms of an arbitrary Kähler potential  <math><mi>K</mi><mfenced><mi>Φ</mi><mover><mi>Φ</mi><mo>¯</mo></mover></mfenced></math> $$ \mathcal{K}\left(\varPhi, \overline{\varPhi}\right) $$ and an arbitrary chiral superpotential  <math><mi>W</mi><mfenced><mi>Φ</mi></mfenced></math> $$ \mathcal{W}\left(\varPhi \right) $$. A general analysis is given to describe the possible interactions of this theory with external higher spin gauge superfields of the (s + 1, s + 1/2) supermultiplet via higher spin supercurrents. It is shown that such interactions do not exist beyond supergravity (s ≥ 2) for any  <math><mi>K</mi></math> $$ \mathcal{K} $$ and  <math><mi>W</mi></math> $$ \mathcal{W} $$. However, we find three exceptions, the theory of a free massless chiral, the theory of a free massive chiral and the theory of a free chiral with linear superpotential. For the first two, the higher spin supercurrents are known and for the third one we provide the explicit expressions. We also discuss the lower spin supercurrents. As expected, a coupling to (non-minimal) supergravity (s = 1) can always be found and we give the generating supercurrent and supertrace for arbitrary  <math><mi>K</mi></math> $$ \mathcal{K} $$ and  <math><mi>W</mi></math> $$ \mathcal{W} $$. On the other hand, coupling to the vector supermultiplet (s = 0) is possible only if  <math><mi>K</mi><mspace width="0.25em"></mspace><mo>=</mo><mi>K</mi><mfenced><mrow><mover><mi>Φ</mi><mo>¯</mo></mover><mi>Φ</mi></mrow></mfenced></math> $$ \mathcal{K} = \mathcal{K}\left(\overline{\varPhi}\varPhi \right) $$ and  <math><mi>W</mi><mo>=</mo><mn>0</mn></math> $$ \mathcal{W}=0 $$.

Interaction of supersymmetric nonlinear sigma models with external higher spin superfields via higher spin supercurrents

We continue the program of constructing cubic interactions between matter and higher spin supermultiplets. In this work we consider a complex linear superfield and we find that it can have cubic interactions only with supermultiplets with propagating spins j = s + 1, j = s + 1/2 for any non-negative integer s (half-integer superspin super-multiplets). We construct the higher spin supercurrent and supertrace, these compose the canonical supercurrent multiplet which generates the cubic interactions. We also prove that for every s there exist an alternative minimal supercurrent multiplet, with vanishing supertrace. Furthermore, we perform a duality transformation in order to make contact with the corresponding chiral theory. An interesting result is that the dual chiral theory has the same coupling constant with the complex linear theory only for odd values of s, whereas for even values of s the coupling constants for the two theories have opposite signs. Additionally we explore the component structure of the supercurrent multiplet and derive the higher spin currents. We find two bosonic currents for spins j = s and j = s + 1 and one fermionic current for spin j = s + 1/2.

Pavel Kočí

Rikard Unge

Higher spin superfield interactions with complex linear supermultiplet: conserved supercurrents and cubic vertices

We present a new method of deriving the off-shell spectrum of supergravity and massless 4D,  <math><mi>N</mi></math> $$ \mathcal{N} $$ = 1 higher spin multiplets without the need of an action and based on a set of natural requirements: (a.) existence of an underlying superspace description, (b.) an economical description of free, massless, higher spins and (c.) equal numbers of bosonic and fermionic degrees of freedom. We prove that for any theory that respects the above, the fermionic auxiliary components come in pairs and are gauge invariant and there are two types of bosonic auxiliary components. Type (1) are pairs of a (2, 0)-tensor with real or imaginary (1, 1)-tensor with non-trivial gauge transformations. Type (2) are singlets and gauge invariant. The outcome is a set of Diophantine equations, the solutions of which determine the off-shell spectrum of supergravity and massless higher spin multiplets. This approach provides (i ) a classification of the irreducible, supersymmetric, representations of arbitrary spin and (ii ) a very clean and intuitive explanation to why some of these theories have more than one formulations (e.g. the supergravity multiplet) and others do not.