Pith. sign in

REVIEW 27 cited by

Wall-crossing, Hitchin Systems, and the WKB Approximation

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 0907.3987 v2 pith:LV6KZ6PI submitted 2009-07-23 hep-th math.DG

classification hep-thmath.DG
keywords riemannspacessystemswall-crossingapproximationbundlescoordinatefield
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

We consider BPS states in a large class of d=4, N=2 field theories, obtained by reducing six-dimensional (2,0) superconformal field theories on Riemann surfaces, with defect operators inserted at points of the Riemann surface. Further dimensional reduction on S^1 yields sigma models, whose target spaces are moduli spaces of Higgs bundles on Riemann surfaces with ramification. In the case where the Higgs bundles have rank 2, we construct canonical Darboux coordinate systems on their moduli spaces. These coordinate systems are related to one another by Poisson transformations associated to BPS states, and have well-controlled asymptotic behavior, obtained from the WKB approximation. The existence of these coordinates implies the Kontsevich-Soibelman wall-crossing formula for the BPS spectrum. This construction provides a concrete realization of a general physical explanation of the wall-crossing formula which was proposed in 0807.4723. It also yields a new method for computing the spectrum using the combinatorics of triangulations of the Riemann surface.

Discussion (0). Sign in to comment.

Forward citations

Cited by 27 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Three-dimensional TQFTs from Argyres--Douglas theories via the 3d/3d correspondence

    hep-th 2026-07 conditional novelty 7.0 of 10

    The twisted circle reduction of the (A1,A2n) Argyres-Douglas theory is realized as a DGG abelian Chern-Simons-matter theory on the lens space L(2n+3,2k), with maximal (one-less-than-maximal) monopole superpotential fl...

  2. Higgsless Lagrangian SCFTs and Strongly Finite VOAs

    hep-th 2026-07 conditional novelty 7.0 of 10

    Higgsless Lagrangian N=2 SCFTs are sparse (free vectors, one SO/USp quiver family, three sporadics); the VOAs of two sporadics are strongly finite and logarithmic.

  3. 5d Trinions and Tetraons

    hep-th 2026-05 accept novelty 7.0 of 10

    The authors construct 5d SCFT trinions and tetraons with D flavor symmetry via M-theory, producing non-linear quivers with instanton symmetry enhancement and ruling out E-type cases.

  4. TBA equations for $SU(r+1)$ quantum Seiberg-Witten curve: higher-order Mathieu equation

    hep-th 2026-04 unverdicted novelty 7.0 of 10

    TBA equations are derived for the higher-order Mathieu equation of the SU(r+1) quantum Seiberg-Witten curve, with an analytic effective central charge and subleading agreement with the WKB method.

  5. Weyl Anomaly Coefficients of Holographic Defect CFTs at Weak and Strong Coupling

    hep-th 2026-04 unverdicted novelty 7.0 of 10

    The type-A Weyl anomaly coefficient b for holographic defect CFTs is negative in a finite parameter region at both weak and strong coupling, providing the first explicit example of an interacting unitary dCFT with b<0.

  6. Compactifying the Sen Action: Six Dimensions

    hep-th 2026-04 conditional novelty 7.0 of 10

    A consistent Kaluza-Klein reduction of the two-metric Sen action needs zero-modes of both Laplacians, while the extra fields are locally removable on-shell.

  7. On the monodromy of KZ-connections with irregular singularities

    hep-th 2026-03 unverdicted novelty 7.0 of 10

    KZ connections with irregular singularities have monodromies that realize topological invariants of links and tangles.

  8. Holographic interpolations of defect CFTs

    hep-th 2025-12 unverdicted novelty 7.0 of 10

    A D5-D7 brane configuration in AdS5 x S5 provides an interpolating holographic dual for defect CFTs, with anomaly cancellation and a conjectured SYM solution.

  9. Generalised 4d Partition Functions and Modular Differential Equations

    hep-th 2025-12 unverdicted novelty 7.0 of 10

    Generalized Schur partition functions Z_USp(2N)(q; alpha) for 4d N=2 USp(2N) theories satisfy order-(N+1) MLDEs with vanishing Wronskian index, alpha fixing MLDE parameters, with links to RCFT characters and a conject...

  10. Eigenfunctions of deformed Schr\"odinger equations

    hep-th 2025-11 conditional novelty 7.0 of 10

    Explicit entire eigenfunctions are constructed for the difference operators 2Λ^N cosh(p)+V_N(x) with arbitrary polynomial potential; they become square-integrable only at a discrete set of energies.

  11. $Q$-operators, $q$-opers, and R-matrices in 5d $\mathcal{N}=1$ gauge theory

    hep-th 2025-07 conditional novelty 7.0 of 10

    In 5d N=1 U(N) gauge theory, codimension-two defects produce Q-operators whose q-difference equations are the Baxter TQ equations of XXZ spin chains built on bi-infinite evaluation modules of quantum affine algebras.

  12. Controlled Chaos in 4D SCFTs

    hep-th 2026-06 unverdicted novelty 6.0 of 10

    Orbifolds of N=4 SYM produce SCFTs whose dilatation operator in a subsector is realized by a tunable spin chain whose eigenvalue statistics exhibit chaos for specific marginal couplings.

  13. Tropical WKB asymptotics of NRS coordinates for opers in $SU(2)$, $N_f=4$ theory

    hep-th 2026-06 unverdicted novelty 6.0 of 10

    Tropicalization of exact WKB formulae for NRS coordinates on the four-punctured sphere yields chamberwise agreement with Seiberg-Witten periods of SU(2) Nf=4 in unimodular primitive-symplectic chambers.

  14. Shading A-polynomials via huge representations of $U_q(\mathfrak{su}_N)$

    hep-th 2026-05 unverdicted novelty 6.0 of 10

    Authors propose shaded A-polynomials A_a(ℓ_b, m_c) for SU(N) via CG chords from huge representations of U_q(su_N) in the classical limit, with examples for knots 3_1, 4_1, 5_1 in su_3.

  15. From classical Lax ODEs to quantum integrable theories: the moduli

    hep-th 2026-05 unverdicted novelty 6.0 of 10

    The paper derives moduli-modified functional relations for Wronskians of a classical Lax ODE that identify quantum states, produce Y-systems and TBA equations without scattering theory, and prove two Zamolodchikov con...

  16. Classical correlation functions at strong coupling from hexagonalization

    hep-th 2026-05 unverdicted novelty 6.0 of 10

    In the classical strong-coupling regime, half-BPS correlation functions in planar N=4 SYM exponentiate under the hexagon formalism and are governed by TBA equations structurally equivalent to Gaiotto-Moore-Neitzke equ...

  17. TBA equations for $SU(r+1)$ quantum Seiberg-Witten curve: higher-order Mathieu equation

    hep-th 2026-04 unverdicted novelty 6.0 of 10

    Derives TBA equations for the higher-order Mathieu equation of the SU(r+1) quantum Seiberg-Witten curve, obtains an analytic effective central charge from Y-function boundary conditions at theta to -infinity, and veri...

  18. On non-relativistic integrable models and 4d SCFTs

    hep-th 2026-04 unverdicted novelty 6.0 of 10

    Generalized Schur indices of N=2 class S theories are expressed using eigenfunctions of non-relativistic elliptic Calogero-Moser models, with extensions claimed for N=1 SCFTs via limits of models like Inozemtsev.

  19. Weyl Anomaly Coefficients of Holographic Defect CFTs at Weak and Strong Coupling

    hep-th 2026-04 unverdicted novelty 6.0 of 10

    Holographic co-dimension-two defect CFTs have type-A Weyl anomaly coefficient b negative in a finite parameter region, with weak–strong agreement for type-A and type-B coefficients in a limit.

  20. Supersymmetric zeta functions and determinants

    hep-th 2025-11 conditional novelty 6.0 of 10

    Residues and special values of supersymmetric zeta functions (built from single-particle indices) are conjectured to reproduce anomaly coefficients, Casimir energies, and central charges across 2d/4d/6d.

  21. Anomaly-induced vanishing of brane partition functions

    hep-th 2025-10 conditional novelty 6.0 of 10

    Anomalies imply vanishing brane partition functions; this yields unified derivations of the Freed-Witten and M5 shifted-quantization conditions and new S-fold D3-brane constraints.

  22. On W-algebras and ODE/IM correspondence

    hep-th 2025-08 conditional novelty 6.0 of 10

    The eigenvalues of quantum KdV-type charges in Virasoro, W3, and W4 algebras are computed from Bethe roots via WKB periods of Catalan curves, verified against direct CFT diagonalization.

  23. Compactifying the Sen Action: Six Dimensions

    hep-th 2026-04 unverdicted novelty 5.0 of 10

    Compactification of the two-metric Sen action requires zero modes from both KK towers but preserves correct on-shell degrees of freedom without doubling.

  24. Central Charges and Vacuum Moduli of 2d $\mathcal{N}=(0,4)$ Theories from Class $\mathcal{S}$

    hep-th 2025-12 unverdicted novelty 5.0 of 10

    Proposes conjectural central charge formulas for 2d N=(0,4) theories from class S reductions and verifies agreement via Hilbert series on special and twisted Higgs branches for SU(2) cases.

  25. Global symmetries: locality, unitarity, and regularity

    hep-th 2025-11 unverdicted novelty 5.0 of 10

    Authors introduce an observable measuring non-locality properties of symmetry operators that encodes fusion algebra information for a class of examples in QFT.

  26. Les Houches Lectures on Exact WKB Analysis and Painlev\'e Equations

    math-ph 2025-12 unverdicted novelty 3.0 of 10

    Lecture notes review exact WKB analysis for ODEs and its combination with topological recursion and isomonodromy to compute monodromy and resurgent structures for Painlevé equations.

  27. Spectral Networks: Bridging higher-rank Teichm\"uller theory and BPS states

    math-ph 2024-11 unverdicted

    A comprehensive introduction to spectral networks that develops higher-rank Teichmüller theory in parallel with class S gauge theory and BPS spectra.

Pith tools