Refined, Motivic, and Quantum

By Tudor Dimofte, Sergei Gukov. 2009

159 citations recorded by the source corpus.

It is well known that in string compactifications on toric Calabi–Yau manifolds one can introduce refined BPS invariants that carry information not only about the charge of the BPS state but also about the spin content. In this paper we study how these invariants behave under wall crossing. In particular, by applying a refined wall crossing formula, we obtain the refined BPS degeneracies for the conifold in different chambers. The result can be interpreted in terms of a new statistical model that counts “refined” pyramid partitions; the model provides a combinatorial realization of wall crossing and clarifies the relation between refined pyramid partitions and the refined topological vertex. We also compare the wall crossing behavior of the refined BPS invariants with that of the motivic Donaldson–Thomas invariants introduced by Kontsevich–Soibelman. In particular, we argue that, in the context of BPS state counting, the three adjectives in the title of this paper are essentially synonymous.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f4e533482ee6a5475dea25678d4a5c256681a9d0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. B. Pioline
2. Ashoke Sen
3. C. Vafa
4. C. Kozçaz
5. Andrew Neitzke
6. Sara Pasquetti
7. N. Wyllard
8. Balázs Szendrői

In Nuclear and High Energy Physics

1. B. Pioline
2. Ashoke Sen
3. C. Vafa
4. Sara Pasquetti
5. S. Cecotti
6. C. Kozçaz
7. Andrew Neitzke
8. N. Wyllard

In Statistical and Nonlinear Physics

1. B. Pioline
2. Ashoke Sen
3. C. Vafa
4. S. Cecotti
5. Sara Pasquetti
6. C. Kozçaz
7. Andrew Neitzke
8. N. Wyllard

Citations in the corpus

• Wall crossing from Boltzmann black hole halos (2010, background): “69) In particular, the primitive wall-crossing formula takes the form[15, 33]”
• R-Twisting and 4d/2d Correspondences (2010, background): “Furthermore, a more refined q-deformed version (taking into account the spin of BPS states), has been advanced in [5, 6], and proven for N = 2 theories which arise from M5-branes in [7].”
• Framed BPS states (2010, unknown): “For nonexotic BPS states our PSC is the same as the “refined index” of [8, 10, 11] up to a (convention-dependent) sign.”
• Motivic degree zero Donaldson–Thomas invariants (2009, methodology): “Taking the weight polynomial specialization of the virtual motives of the Hilbert schemes gives a virtual version of the Poincaré polynomials of the Hilbert schemes.”
• A& B model approaches to surface operators and Toda thoeries (2010, background): “In [12] the choice δ = −1 was made, whereas in the later work [50] δ = 0 was argued to be natural.”