2d dualities from 4d

We extend our sincere gratitude to the referees for their meticulous and thoughtful feedback, as well as their time and care in evaluating our manuscript. Their expertise and constructive suggestions have profoundly strengthened the quality of this work.

In addressing the referees’ comments, we have implemented revisions to the manuscript, including:
- We have corrected the superpotentials of some (0,2) theories in Section 3.2 and Appendices C.2–C.4.
- We have also refined the discussion of Higgsing in Section 3.3 for clarity. - Based on the referees' suggestions, we have incorporated further explanatory details and improved the overall presentation and phrasing.

We thank the referees once more for their invaluable guidance, which has been pivotal in elevating the level and clarity of our paper.

We would like to thank the referees for their valuable feedback. In response to their comments and suggestions, we have made the following changes and improvements in the revised manuscript:

• Below equations (2.12) and (2.14), we now highlight and clarify the underlying TQFT structure of the 2d (2,2) theories.
• Below equation (3.9), we have added a discussion comparing our evaluation of the central charge to that of the (0,2) triality for unitary gauge groups. In particular, we emphasize the necessity of performing c-extremization for unitary gauge groups, even though the IR non-linear sigma model has a non-compact target space.
• We corrected the superpotential in equation (3.12), as one of the referees pointed out.
• Similarly, the superpotential in equation (3.21) has been corrected. In particular, we revised the construction of the field A in the Sym-1 theory in response to the referee’s comment.
• Per the referees’ suggestions, we improved the explanation of the Higgsing procedure in Section 3.3. Specifically, we clarified that the specialization (x \to 1) in the elliptic genus corresponds to giving a vacuum expectation value (VEV) to the chiral field (X) in the bottom theory of Figure 6. This leads directly to the duality depicted in Figure 7.
• In Section 4, we now provide a list of 4d theories and the corresponding 2d dualities discussed in the paper. We have also expanded the summary and added clarifying remarks in the conclusion.
• Below equation (B.2), we revised the explanation of the application of c-extremization.
• The superpotentials in equations (C.7), (C.17), and (C.21) have been corrected as per the referee's observation.
• In equations (C.19) and (C.23), we removed the field (B), which was not present in the rest of the text.