2013/06/17 by Sara Angela Filippini, Filippini, Sara Angela, Jacopo Stoppa +1 · 1 citation
Mathematics · Physics and Astronomy · #14N35 #14T05 #35Q15 #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AG #math.MP #msc:14N35 #msc:14T05 #msc:35Q15
paper · pdf · doi:10.48550/arxiv.1306.3852
26 pages, 3 figures
arxiv created 2013/06/17 · arxiv updated 2013/06/18
We revisit the wall-crossing behaviour of solutions to the Thermodynamic Bethe Ansatz type equations arising in a class of three-dimensional field theories, expressed as sums of "instanton corrections". We explain how to attach to an instanton correction at a critical value a set of (combinatorial types of) tropical curves in R2 of fixed degree, which determines its jump to leading order. We show that a weighted sum over all such curves is in fact a tropical count. This goes through to the q-deformed setting. Our construction can be regarded as a formal mirror symmetric statement in the framework proposed by Gaiotto, Moore and Neitzke.