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My paper on lattice chiral fermion theory was rejected by two RRL referees (very strongly) and by a PRL editor."The reason for skepticism is the long history of past failures" (none by me). The editor did not say that "The reason for skepticism is the long history of past failures of the author", which would be more relevant.

[This paper is now published in Chinese Physics Letter (arXiv:1305.1045).]

The arguments for the main result of the paper is really simple, and can be easily presented within one page. Maybe, I am too easily convinced. When I am convinced to see something, it may not be convincing enough for some other people.

The following are the referee's reports and my reply, and the editor's report.

My point is:

走自己的路，欣赏自己的工作，看重自己的工作，是科学工作者对待科研的一种心态。

“写出来的文章，至少要得到自己的认可。最重要的也是得到自己的认可。自己看重自己的文章。这样别人不认可，也不会信心全无。写文章的目的，不是为了发表，是为了满足自己的好奇心。以此为目的，容易出好文章，容易发表。”

===================================================

Lattice non-perturbative definition of an SO(10) chiral gauge theory

and its induced standard model (arXiv:1305.1045)

by Xiao-Gang Wen

----------------------------------------------------------------------

Report of Referee A and my reply

----------------------------------------------------------------------

Referee A:

In this letter, the author is proposing a non-perturbativelattice

formulation of (anomaly-free) chiral gauge theories. This problem

itself is of broad theoretical interest and if a convincing solution

is given, it will be of great importance.

Reply:

I agrees with the referee A that the non-perturbative lattice formulation of

(anomaly-free) chiral gauge theories is of broad theoretical interest and of

great importance.

Referee A:

However, what one finds in this letter are a very general description of the

problem in more than 2 pages and a very brief sketch of the idea in almost

half page. I myself cannot believe this naive idea does solve the problem of,

for example, the breaking of the gauge symmetry with finite lattice spacings.

Reply:

In the 2 pages of the paper, I reviewed

1) a recent break through in condensed matter physics -- a classification of

SPT states

2) a realization that the SPT phases classify the gauge anomalies in one lower

dimension.

This two results do solve the problem of the breaking of the gauge symmetry

with finite lattice spacings. To see this, we note that the anomaly-free

condition imply that the SPT state in the bulk is trivial, and trivial SPT

state can have a gapped boundary that do not break the symmetry. Once we

understand the above two results and once we believe that the right-hand Weyl

fermions coupled to SO(10) gauge theory is free of all gauge anomalies, then

it is almost trivial to put right-hand Weyl fermions coupled to SO(10) gauge

theory on a lattice, which I spend one page of the paper to explain. So the

key progress is the above two mentioned results, which were explained in

several recent (very) long papers (refs [32,41,25] in the new vertion). This

short paper is a direct and natural application of those recent results.

Referee A:

In any case, one cannot even judge whether this idea works

or not from the description in this letter, because no precise form of

the idea (for example, what is the precise form of the underlying

4-dimensional lattice hamiltonian, how to introduce the gauge

interaction, or how the anomalous cases are distinguished from the

anomaly-free cases etc.) is not given. From these reasons, I think

this letter is not suitable for publication in Physical Review

Letters.

Reply:

In the new version, I added a section in supplemental material to give a more

detailed description of the lattice model in 4D space. Such a construction is

well known, so I did not include it in the main text. I also explained how to

introduce the gauge interaction (by simply gauging the SO(10) global

symmetry).

"how the anomalous cases are distinguished from the anomaly-free cases" is a

very good question. To stress this issue, I added a generalization of the

SO(10) result as conjecture in the new version (in a box on page 2). I also

added a few examples on page 4, which demonstrate that our approach

does not apply for the known anomalous chiral theories.

----------------------------------------------------------------------

Report of Referee B and my reply

----------------------------------------------------------------------

Referee B:

I regret having to say this, but the manuscript fails to satisfy the most

minimal requirements for a scientific publication.

All the author can offer is, literally, wishful thinking. The manuscript

contains no study of any kind -- neither analytic nor numerical --to support

the author's proposal. That proposal is not even well defined (see below). I

hate to say this but this is a rare case of "not even wrong" -- the manuscript

does not even contain any attempt to do scientific work of any kind that would

support the claims, or hopes, of the author.

Reply:

According to Referee A, the non-perturbative lattice formulation of

(anomaly-free) chiral gauge theories is of broad theoretical and of great

importance. In this paper, I claim that right-hand Weyl fermions in

16-dimensional representation of SO(10) coupled to SO(10) gauge field can be

put on a lattice of the same dimension (without breaking the SO(10) gauge

symmetry on lattice), if we just allow lattice fermion to directly interact.

Such a claim can be wrong (and the referee B try to argue that the claim is

indeed wrong). So this paper is not "not even wrong". In the new version,

the key claims of the paper are put into three boxes.

It is also not fair to say "the manuscript does not even containany attempt

to do scientific work of any kind that would support the claims, or hopes, of

the author". In this paper, I showed that

1) There is a (SO(10) symmetry breaking) Higgs field that give all 16 Weyl

fermions a mass

2) The target space of the Higgs field generated by the SO(10) rotation is a

9D sphere, S_9, which have a trivial homotopy group pi_d(S_9) for d<9.

The above two results allow me to argue that the Higgs field can be in a

disordered phase (that do not break the SO(10) symmetry) while still give the

fermions (the doublers) a mass. (See the discussion on the first half of page

4 in the new version.) These two simple arguments lead to the result (the

claim) of this paper.

Referee B:

The problem of constructing lattice chiral gauge theories is a

long-standing one. The proposal put forward by the author is basically

a variant of the Eichten-Preskill model [14].

Reply:

Indeed, the proposal put forward is basically a variant of the

Eichten-Preskill model. The new features of this paper are the two simple

arguments mentioned above. This leads to a new way to design the fermion

interaction, which, in turn, leads to the result of this paper.

(added later: The mirror fermion approach of Eichten-Preskill

some times works and some times does not work. This paper provides a sufficient condition for the

mirror fermion approach to work, ie for interaction to gap out the mirror sector without breaking the symmetry.)

Referee B:

This model was studied in detail by Golterman, Petcher and Rivas[20], where

the main questions were identified, and extensive evidence pointed to the

failure of the model. Other models were proposed that were found to fail for

similar reasons later on, whereas completely different approaches lead to at

least partial success.

Reply:

In the paper by Golterman, Petcher and Rivas, it was stated that "because of

the presence of a symmetry breaking phase transition, the scenario envisioned

by Eichten and Preskill will most likely not be realized." The claim of

Golterman, Petcher and Rivas, "most likely not be realized", does not

logically contradict with the claim of this paper, "be realized". Golterman,

Petcher and Rivas studied a particular fermion interaction. They showed that,

for such an interaction, to make all the doublers massive, one has to break

the symmetry. Based on the new ideas of SPT phases and their relation to gauge

anomalies, this paper propose a new way to design a fermion interaction. Such

a fermion interaction should give all the doublers a mass without break the

symmetry. The new way to design the fermion interaction is the new result of

this paper.

In other words, Golterman, Petcher and Rivas considered one particular

interaction, and show that it does not works. In this paper, we argue that there

is another interaction that should work. There is no contradition.

Referee B:

As far as I can tell from this manuscript, the author is not even

aware of what are the main issues. Just like Eichten and Preskill, the

author wishes to find a symmetric phase with a chiral spectrum. This

cannot possibly be the weak-coupling symmetric (PMW) phase, so the

hope is for a strong-coupling symmetric (PMS) phase in which the

scalar field will have zero vacuum expectation value, while the

spectrum will remain chiral in the continuum limit. The mechanism that

can, and does, leads to a failure is the formation of bound states of

the lattice fields that become additional elementary fermions in the

continuum limit. In particular, ref [20] provided conclusive evidence

that this is what happens in the PMS phase of the Eichten-Preskill

model: because of the bound-states formation, the continuum-limit

spectrum consists of Dirac fermions; it is not chiral.

As I said, the author does not even seem to be aware that this is the

main question. That this is the question he should be addressing would

have been clear to anyone who really studied the literature --the

original papers and/or review articles. References to all this

literature can be found for example in the recent series of papers by

Poppitz et al [17,22].

Reply:

It is indeed clear to every one that weak-coupling symmetric (PMW) phase does

not work. Golterman-Petcher-Rivas and other papers provided conclusive

evidence that a strong-coupling symmetric (PMS) phase also does notwork, for

a particular form of fermion interaction. This paper suggests a new way to

design fermion interaction which I believe should work (ie to give all

doublers an energy gap without breaking the symmetry), based on the insights

from the SPT states and their relation to gauge anomalies.

I showed that

1) There is a (SO(10) symmetry breaking) Higgs field that give all16 Weyl

fermions a mass

2) The target space of the Higgs field generated by the SO(10)rotation is a

9D sphere, S^9, which have a trivial homotopy group pi_d(S^9) ford<9.

The above two results allow me to argue that the Higgs field can bein a

disordered phase (that do not break the SO(10) symmetry) while still give the

fermions (the doublers) a mass. (See the discussion on the first half of page

4 in the new version.) These two simple arguments lead to the result (the

claim) of this paper.

(Added later: The weak interaction limit (PMS) does not work. The infinite interaction limit (PMS) does not work. But the proper interaction proposed in this paper is between the two limits. The proper interaction strength is of the lattice cut-off energy scale.)

Referee B:

The author talks about a hamiltonian approach instead of the common euclidean

path integral. However, the physics issues are the same, and as I noted, the

author did not do any work what so ever, let alone any work that would suggest

that a hamiltonian approach would help in any way.

Reply:

I agree with the referee B that hamiltonian lattice approach and space-time

lattice approach are similar. I stressed the hamiltonian lattice approach

in order to state the result (the claim) of this paper clearly.

As I mention above, I did do some new work in this paper: the two simple

arguments listed above. I like to add that I am surprised that such simple

arguments can lead to a solution of the long standing problem of putting some

anomaly-free chiral gauge theories on lattice. I guess the insights from SPT

states and the new understanding of anomalies help a lot.

I try to explain those insights in the first two pages of the paper.

Referee B:

The author adds a fourth space dimension so that there are chiral fields on

the three dimensional spatial boundaries in the free theory case. This putting

together of domain-wall fermions and the Eichten-Preskill proposal had been

tried in the past, and once again it was found to fail for similar reasons.

Because of the extra space dimension, the author has to make up his mind

whether or not the gauge field depends on this extra dimension. There is no

word on this, so that the proposal is not even well defined. In the

literature, both approaches had been tried, and the existing evidence points

to a failure in both cases.

Reply:

I have stressed in the paper that the extra dimension is finite. The 4+1D

lattice theory is really a 3+1D lattice theory. In this case, I do not have

to make up my mind whether or not the gauge field depends on this extra

dimension, since both assumptions lead to local 3+1D lattice gauge theory. I

like to repeat that this paper suggests a new way to design fermion

interaction which I believe should work (ie to give all doublers anenergy gap

without breaking the symmetry), based on the insights from the SPT states and

their relation to gauge anomalies.

Referee B:

It is the author's burden to prove by scientifically sound calculations that

he can do better.

Reply:

The two arguments listed above are scientifically sound calculations, although

they are very simple. There is indeed a logical gap between the two arguments

and the claim of this paper. I myself is convinced that the two arguments

lead to the claim of this paper. The approach in this paper lead to a design

of fermion interaction. One can confirm or disapprove my judgement by future

numerical calculations. I myself plan do some numerical calculations in the

future, motivated by the approach of this paper.

I am a condensed matter physicist, and I am sorry that I cannot write a paper

from an angle of lattice gauge physicists. But I feel that a new angle to look

at the long standing chiral-fermion problem should be useful, that may lead to

a breakthrough as I try to argue in this paper.

----------------------------------------------------------------------

Report of the Divisional Associate Editor

----------------------------------------------------------------------

This paper claims to have solved the important, long-standingproblem

of formulating a chiral gauge theory non-perturbatively onthe

lattice. It has been reviewed by two referees, who both recommend

rejection. I have then been contacted, because the author has appealed

the rejection.

I have hesitated for a long time about what to recommend, and I

apologize for this delay. In the end, I agree with the previous

referees: it seems to me that, in spite of its novelty, the paper

should not be published in Phys. Rev. Letters. A publication in PRL

would mislead the readers by conveying the notion that this paper

presents a solution to the formulation of a chiral lattice gauge

theory. In my opinion, the paper presents a proposal to be tested,

rather than a solution.

The reason for skepticism is the long history of past failures.The

proposal put forward by the author belongs to the family of "mirror

fermions", with the new ingredient of symmetry-protected topological

order. It is not at all clear to me that this new ingredient

guarantees success. In particular, the most recent attempt,Ref.22

(arXiv:1211.6947v3), shows failure of the mirror fermions to decouple,

for no obvious reason. This finding should motivate all of us,

including the author, to consider new claims with caution.

http://blog.sciencenet.cn/blog-1116346-736247.html

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