Mirror Symmetry for New Physics beyond the Standard Model in 4D Spacetime
Round 1
Reviewer 1 Report
The author provides a prospect evaluation of mirror symmetries as candidates for extra standard model theories. The text is well written and pedagogical, albeit lacking originality as compared to other works. Under the right context as defined by the editors, i support the publication of this review/letter article. Some comments for improvement:
a. Please enhance the contribution or at least talking points of this work in the last paragraph of the introduction, As I understand this is only done after "Here" and it is only one sentence. It is my estimate that the work will be improved with a sort of elaborate introduction on what is included in this work i.e. which models and why.
b. Maybe the impact of this discussion can be increased if some bridge is made towards condensed matter and/or geometrical interpretations possible references include https://doi.org/10.1103/PhysRevB.98.155419, https://doi.org/10.1146/annurev-conmatphys-040721-021029
c. Section 2 cite other discussions of irreducible representations of O(1,n), even if rare as you mention.
d. In the conclusions maybe emphasize some precise points that are made in this work, it is a bit general.
e. What about models that are not discussed here? I like how each model discusses has a motivation but what about also some more critical discussion on models that are weak candidates etc.
Author Response
Please see the attachment
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The four topologically distinct components of O(1, 3) are generated by the two discrete generators of the entire Lorentz group O(1, 3) in 4D spacetime. These, however, are commonly chosen to be parity inversion symmetry P and time reversal symmetry T. Mirror symmetry is particularly important since it effectively creates a new sector of mirror particles. It doubles the whole Dirac fermion representation in QFT (Quantum Field Theory). Its intimate relationship to Calabi-Yau mirror symmetry and T-duality in string theory is made clear. Then, by using both left- and right-handed heterotic strings led by mirror symmetry, extensions beyond the Standard model can be built, as the author explained in this article.
The author discusses a number of significant implications, including supersymmetry, chiral anomalies, topological transitions, the Higgs boson, neutrinos, and dark energy. A well-written introduction and appendix are included with the article "ELEMENTARY PARTICLES AND MIRROR SYMMETRY" to fully describe irreducible representations of the entire O(1, n) group. They then compare the results with those from string theory in order to comprehend this mirror symmetry better. In order to drastically change the original knowledge of string theory and reinterpret it in the light of the new framework. The author focuses primarily on comprehending the mathematical constructions in string theory and relating these mathematical conclusions to physical interpretations in mirror matter theory. But these linkages imply that string theory might be a highly powerful and promising instrument for furthering the development of the new mirror theory.
The construction of certain fermion condensation models, such as the Nambu-Jona-Lasinio (NJL) mechanism utilizing four-fermion interactions and perhaps the Sachdev-Ye-Kitaev (SYK) model via random interactions of multiple fermions. This is suggested by the description of low-dimensional supersymmetric mirror models and string theory. The author demonstrates that ordinary and mirror sectors share the same set of neutrinos for higher dimensional supersymmetric mirror models. According to the author, in the Dark energy and Higgs mechanisms, the mirror sector is right-moving or anti-holomorphic whereas the regular sector is left-moving or holomorphic. Also explained are chiral anomalies and topological transitions.
The fact that each sector (ordinary and mirror) of the gauge groups described above exhibits a built-in supersymmetry between matter fermions and gauge bosons is one of their most striking characteristics. This is unlike normal investigations of supersymmetry, which frequently add a new set of SUSY particles, and is due to the fact that both the fermion and boson degrees of freedom are identical. A novel strategy is based on the observation of a matching of degrees of freedom between fermions and bosons in many models, and is comparable to the quasi-SUSY principle that Nambu presented. Mirror symmetry, not supersymmetry, is most likely responsible for the Standard Model's known particles' seeming doubles.
It is shown that mirror symmetry is a crucial component of the whole Lorentz group and beyond. One could think of T-duality and Calabi-Yau mirror symmetry in string theory as specific examples of the more abstract idea of mirror symmetry. There are numerous other linkages between string theory and supersymmetric mirror models that are examined. The new mirror matter theory can be further developed using string theory, which is undoubtedly a highly powerful mathematical tool. Understanding the dynamics of spacetime's dimensional phase transitions may also be aided by other proposed quantum gravity theories and fermion condensation models. I advise publishing this review or commentary article as it is.
Author Response
I'd like to thank the reviewer for their nice comments and precise summary of the main contributions of this paper. I hope that this piece of work will stimulate further efforts to apply string theory to the development of the new mirror matter theory.
