Description:
In these files we study the classification of 5d Superconformal Field Theories arising from brane webs in Type IIB String Theory, using a Siamese Neural Network to identify different webs giving rise to the same theory. We consider two datasets of brane webs with three external legs: one with classes defined under weak equivalence and the other defined under strong equivalence, where weak and strong equivalence are defined as
Strong equivalence: two webs are strongly equivalent if they can be transformed into each other by means of any combination of SL(2,Z) and HW moves.
Weak equivalence: two webs are weakly equivalent if they have the same number of 7-branes, asymptotic charge invariant and total monodromy up to SL(2,Z).
How to run:
The 2x3 web matrices describing the brane webs of the two weakly and strongly equivalent datasets are saved in the files 3leg_data_X.db and 3leg_data_Y.db respectively. The SNN can be trained and tested by running the SNN.py file and the TDA can be obtained by running the TDA.py file.
In addition to the databases used for the investigation, a further larger database was generated WebData_[5, 5, 5, 2, 100].pickle.zip, which one can search with the notebook Web_3Leg_DatabaseSearch.ipynb to compute invariants, compare equivalences, and generate equivalent webs for input webs of your choosing. Please download and unzip the data before using, and ensure the data filepath is correct.