On the consistent disformal couplings to fermions

Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: We're looking at the paper: "On the consistent disformal couplings to fermions".

Jocelyn: The gist: Disformal couplings to fermions lead to a unique derivative coupling to the axial fermionic current, which contains higher derivatives in general.

Vera: First, who's behind it and why it matters.

Paper summary: Vera: So we're looking at this paper called "On the consistent disformal couplings to fermions," and what it claims is that these couplings lead to a specific kind of derivative coupling between the disformal fields and the axial fermionic current, which generally has higher derivatives in it.

Jocelyn: Right, so they are looking at how these couplings work with fermions and finding this unique derivative coupling that brings in those higher derivatives. It seems like they're setting up some conditions to keep things consistent without introducing ghosts.

Subrahmanyan: That sounds like a tricky area because higher derivatives often bring in those pesky ghost degrees of freedom, so the focus on consistency is important for cosmology as well, considering how we model dark energy and dark matter one <ref:2510.07419#pg1>.

Vera: Exactly. The core thesis they push for is that to avoid these ghosts, you end up needing some specific conditions on the field space metric if you're using two scalar fields.

Jocelyn: And what they found was that for those two-scalar field disformal transformations, a consistent coupling must have a degenerate field space metric. That opens up avenues for new kind of gravity models where you can still explore modified gravity but keep it ghost-free twelve.

Subrahmanyan: That's interesting because it connects the structure of the transformation directly to the stability of the resulting theory, which is crucial when you're trying to build a model that describes our universe on large scales.

Vera: They then show that this degeneracy condition means that for those two scalar fields, h2 must equal h3, which is the same as b2 equaling b3. This makes the coupling term, called M alpha, depend only on derivatives of the scalar fields X, Q and Z.

Jocelyn: So they're saying that these integrability conditions for the total differential dH lead precisely to the absence of higher time derivatives in those cases forty-three <ref:2510.07419#pg2>.

Subrahmanyan: That really tightens the constraint on how these couplings can behave dynamically; it means you can't just have arbitrary higher derivatives without running into ghosts unless you impose that degeneracy condition.

Paper summary: Vera: Moving on, they also explored a case with a single scalar field but with higher order spatial derivatives, where they consider a disformal transformation like mu nu = f zero g mu nu + f one phi mu phi nu + 2f two phi(mu not equal to nu) + f three delta mu nu.

Jocelyn: And for a consistent matter coupling in that single scalar case, they found that the condition c twenty = -c twenty-one d X implies f3 has to be equal to 2C 2c eleven. This shows that there are still disformal couplings to matter where f3 is not zero and it's consistent.

Subrahmanyan: That’s a bit encouraging because it means the restriction on the transformation form isn't as severe as in the two-scalar case, opening up a larger class of disformal Horndeski theories that we can look at thirty-eight forty-three <ref:2510.07419#pg2>.

Vera: And they extend this idea to single vector fields with higher derivatives in section V, and they demonstrate that these transformations including the field strength are highly restricted.

Jocelyn: Specifically, for a U(one) gauge symmetry, the axial coupling expression M alpha ends up involving second time derivatives multiplied by first derivatives of the vector field <ref:2510.07419#pg1>.

Subrahmanyan: That is significant because from that term in equation ninety-six the equations of motion then contain third derivatives of the vector field, which means they conclude that this disformal coupling with U(one) gauge symmetry is inconsistent with fermions ninety-two.

Vera: So what we have here is a lot about how these couplings interact with different field setups—scalar fields versus vector fields.

Jocelyn: And to wrap up the structure, for two scalar fields, you need that degeneracy condition on the metric space, while for single scalar fields with higher spatial derivatives, the transformation form is much more restricted.

Subrahmanyan: The paper highlights that the formalism can also be applied to single field disformal transformations with higher derivatives and extends conditions from other work thirty-nine <ref:2510.07419#pg2>.

Vera: In essence, they’ve provided a larger class of disformal Horndeski theories by showing how these constraints apply across different setups.

Jocelyn: And for vector fields, they managed to propose a new class of transformations for higher derivative Proca theories that are free of ghost degrees of freedom fifty-eight fifty-nine <ref:2510.07419#pg3,propose a new class of transformations for higher derivative Proca theories>.

Subrahmanyan: So the implication is that we can construct viable disformal transformations even in more complex setups like single vector fields, provided we stick to these restrictions.

Paper summary: Vera: It seems like the main thing they're pointing toward is how these couplings can be used to construct new modified gravity models by performing the inverse transformation.

Jocelyn: And they emphasize that if the metric transformation is invertible, the number of degrees of freedom doesn't change, which means the resulting model can be free of Ostrogradsky ghosts as long as there were no ghosts to begin with thirty-four thirty-five <ref:2510.07419#pg2,free of Ostrogradsky ghosts as long as there were no ghosts to>.

Subrahmanyan: It really boils down to how you treat those higher-derivative interactions in the gravitational sector when you introduce this disformal coupling.

Vera: So, if we look at the title of "On the consistent disformal couplings to fermions," it suggests a deep dive into making sure these couplings are physically sound with matter fields.

Jocelyn: And for someone who only listens to this, it means that constructing viable modified gravity models using disformal transformations depends heavily on imposing specific degeneracy conditions based on the number of scalar fields you're using.

Subrahmanyan: This work gives us a concrete set of rules about when these couplings lead to higher derivatives and when they stay within the bounds of what we consider consistent theories.

Vera: So, to bring it all together, this paper shows that for two scalar fields you need to impose degeneracy conditions on the form of the field space metric.

Jocelyn: And in contrast, for single scalar field disformal transformation with higher derivatives, the form of that transformation is highly restricted.

Subrahmanyan: The formalism extends to single field disformal transformations with higher derivatives and leads to a larger class of disformal Horndeski theories based on conditions derived in work like thirty-nine <ref:2510.07419#pg2>.

Vera: And they also managed to construct a viable disformal transformation of a single vector field depending directly on the field strength, which can be used to explore new classes of Proca theories beyond current approaches.

Jocelyn: It seems like the main point is that you can build consistent disformal transformations even in more complex setups, but you have to follow these specific rules about degeneracy or restriction.

Conclusion: Vera: So we've seen how these disformal couplings lead to a specific derivative coupling for fermions, and now we're at the end of this paper, "On the consistent disformal couplings to fermions."

Jocelyn: Right, so what does that title actually mean when you read it? It sounds pretty technical.

Subrahmanyan: It means they’re figuring out how these couplings have to behave consistently with matter fields, which is a big deal because we need models that don't have ghosts.

Vera: Exactly. The main point here is about the constraints they put on these couplings, especially when you look at different setups, like two scalar fields versus one.

Jocelyn: And what are those constraints? I'm guessing it involves some kind of metric structure or something that prevents instability.

Subrahmanyan: They show that for two scalar fields, you have to impose a degeneracy condition on the field space metric for the coupling to be consistent and avoid those higher-derivative ghosts.

Vera: That’s right, they found that if you're using two scalars, h2 has to equal h3, which simplifies the coupling term significantly.

Jocelyn: So it boils down to a specific relationship between those field components, rather than letting you pick anything arbitrarily.

Subrahmanyan: And for single scalar fields with higher spatial derivatives, the paper shows that the form of that transformation is actually much more restricted than in the two-scalar case.

Vera: That's a key difference they point out; the restrictions are different depending on how many fields you start with or if you're looking at spatial versus temporal derivatives.

Jocelyn: So, what does this mean for us when we think about building modified gravity models?

Subrahmanyan: It gives us a roadmap. You can build viable theories like disformal Horndeski theories by following those specific conditions they derived from the consistency checks.

Vera: And for vector fields, they found a way to construct a viable transformation that depends directly on the field strength, which is useful for exploring Proca theory ideas.

Jocelyn: So it sounds like this paper is really about showing that even in these complex setups, we can still find physically sound ways to couple gravity and matter.

Subrahmanyan: It’s about setting the rules for consistency so that the resulting theories are actually workable models for cosmology and structure formation.