Is the massless survivor of an SMG gapped phase genuinely chiral?

[albronco1]

Consider a vector-like lattice gauge theory whose fermion content has Weyl number ≡ 0 (mod 16) i.e. anomaly-free in the sense that admits symmetric mass generation, the 16 of SO(10) / one SM generation being the canonical example tuned near the lower edge of the conformal window. Now switch on a symmetric (mod-16-channel) four-fermion interaction that gaps the "mirror" sector without breaking the chiral symmetries.

My question concerns the nature of the resulting strong-coupling gapped phase:

1. In that phase, is there a genuinely chiral massless survivor — i.e. true *dynamical* decoupling of the mirror or do the mirror two-point-function zeros signal a *kinematically* vector-like spectrum, in the sense of Golterman–Shamir?

2. Does the Golterman–Shamir generalized no-go (their one-particle-Hamiltonian locality/analyticity argument, arXiv:2505.20436) settle this in general, or is there room when the effective one-particle Hamiltonian fails their locality assumptions?

3. What is the current lattice status? Do the SU(2) N_f=4 and SU(3) N_f=8 studies (Catterall, Hasenfratz, et al.) actually distinguish dynamical from kinematic mirror decoupling, or only establish that a symmetric gapped phase exists?

Observables I'd expect to discriminate: the gradient-flow β-function near the edge, the chiral susceptibility (suppressed vs. diverging), the fermion-propagator pole-vs-zero structure, and finite-size scaling of the transition (BKT-type vs. first-order). Pointers to the most current references very welcome.

 

[renormalize]

You are of course free to ask detailed questions here on Physics Forums, but the reality is that this particular one is likely much too specific and technical to get useful feedback from PF. You might be better served by directly contacting one or more of the authors that you mention in your post.

 

[albronco1]

You are of course free to ask detailed questions here on Physics Forums, but the reality is that this particular one is likely much too specific and technical to get useful feedback from PF. You might be better served by directly contacting one or more of the authors that you mention in your post.

Hey, thx for answer I’m independent , that’s why i never thought about to contact this people’s directly. Do you think they will realöy answer ?

Greetz

KF

 

[renormalize]

Hey, thx for answer I’m independent , that’s why i never thought about to contact this people’s directly. Do you think they will realöy answer ?

Write a polite email with your questions to the appropriate authors and see if they answer. What do you have to lose by trying?

 

[albronco1]

Write a polite email with your questions to the appropriate authors and see if they answer. What do you have to lose by trying?

Nothing to lose and I did it let’s see … i mean maybe this questions are also interesting for them, for the next version of SMG , so nothing to lose ;)

 

[albronco1]

Nothing to lose and I did it let’s see … i mean maybe this questions are also interesting for them, for the next version of SMG , so nothing to lose ;)

Wow I can’t believe he really answered… I will see what I can do now with this information :)

 

[ohwilleke]

Hey, thx for answer I’m independent , that’s why i never thought about to contact this people’s directly. Do you think they will realöy answer ?

Greetz

KF

Practicing physicists, in my experience, are almost always willing to discuss their papers and specialties with well-informed people.

 

[albronco1]

Practicing physicists, in my experience, are almost always willing to discuss their papers and specialties with well-informed people.

Yeah but I’m just a LLM „physicist“ but I found some actual problems …

 

[albronco1]

Practicing physicists, in my experience, are almost always willing to discuss their papers and specialties with well-informed people.

Don’t want to make adds but if you are interested I can send you my manuscript ..

 

[albronco1]

BTW if someone is interested in the answer I got, ask me DM

 

[renormalize]

BTW if someone is interested in the answer I got, ask me DM

Is there any reason you can't share here in this thread at least a brief summary of the answer you received, so that everyone may read it?

 

[albronco1]

Is there any reason you can't share here in this thread at least a brief summary of the answer you received, so that everyone may read it?

Hmm it’s a private conservation,so I don’t know …. But when I think about it yeah why not ….
It helped me in the sense that „so it is possible that some clever construction exists that "escapes" our theorem.“
He will contact me again in July because he is now at conferences.. I will see.. if you are curious about my idea I would upload a note about it , but only if it’s allowed ….

Thank you for your interest in our work and for your questions, we're happy to try answer them.

1. In that phase, is there a genuinely chiral massless survivor — i.e. true *dynamical* decoupling of the mirror — or do the mirror two-point-function zeros signal a *kinematically* vector-like spectrum, in the Golterman–Shamir sense?

Yes, it has. In 1986, Eichten and Preskill made a proposal (Nucl.Phys.B 268 (1986) 179-208) that
would now be categorized as an "SMG" proposal. In Nucl.Phys.B 395 (1993) 596-622 it was
shown that the type of bound-state formation we discuss in our paper indeed happens. For the
proposal of Phys.Rev.Lett. 128 (2022) 18, 185301 it has not been studied (and will have to be
done numerically because of the nature of the interaction terms for that proposal).

2. Does your generalized no-go (the one-particle-Hamiltonian locality/analyticity argument, arXiv:2505.20436) settle this in general, or is there room when the effective one-particle Hamiltonian fails the locality assumptions?

Indeed, it is important for any successful proposal to circumvent the assumptions of our nogo theorem.
To date, the only approach we know of that does this is our own "gauge-fixing" proposal, Refs. [21-29] of
our paper. (The fermion propagator was discussed in detail in Ref. [24].) To be clear, our proposal is not
in the SMG category. We have not tried to make an exhaustive study of all possible SMG models, so it
is possible that some clever construction exists that "escapes" our theorem. In this sense, our paper
points to what needs to be studied in any SMG proposal. (Bound states, nature of effective one-particle
Hamiltonian, etc.)

3. What is the current lattice status? Do the SU(2) N_f = 4 and SU(3) N_f = 8 studies (Catterall, Hasenfratz, et al.) actually distinguish dynamical from kinematic mirror decoupling, or only establish that a symmetric gapped phase exists?

This is a class of theories outside the class we studied in our paper, because these theories only have
"standard" gauge interactions, and no specifically designed "irrelevant" SMG interactions. Rather,
there are claims that these theories have non-trivial phase transitions at some non-Gaussian fixed
point into a novel phase that may (or may not) exhibit SMG. It is not at all clear what the nature of the claimed phase transitions is; there are many questions (as basic as whether the theory at the critical point is even
Lorentz invariant) that need to be investigated before anything more specific can be said. We are
skeptical because of all those questions, but the verdict is out. We note that our observations
on propagator zeros remain relevant for any SMG theories, including this class.

Moreover, in the SU(3) N_f = 8 case it has been shown that some of the staggered shift symmetries are broken spontaneously by a bilinear fermion condensate in the relevant phase (see Phys. Rev. D 85, 094509 (2012)). Such a condensate could in fact play the role of (the expectation value of) a mass term (see Nucl. Phys. B 245 (1984) 61). Hence it is not even clear that that phase meets a key criterion of SMG, namely, that fermion mass generation is not accompanied by a bilinear fermion condensate. As for the SU(2) N_f = 4 case discussed in arXiv:2604.02424, to our knowledge the question of shift symmetry breaking has not been studied yet (and, of course, it should).

The observables I would expect to discriminate are the gradient-flow β-function near the edge, the chiral susceptibility (suppressed vs. diverging), the fermion-propagator pole-vs-zero structure, and the finite-size scaling of the transition (BKT-type vs. first-order). Any pointers to the most current references would be very welcome.

In our view, arXiv:2604.02424 (which you mentioned in your email to Yigal) is very confusing, and
raises more questions than clarifies them! We think it's fair to say that it is not a very good place to
start understanding SMG for anyone trying to enter the field. But that is just our opinion!

PS. Because you wrote to both of us, we discussed your questions and combined our answers.