Exact stringy microstates from gauge theories

Self Cite

We study to what extent, and in what form, the notion of gauge-string duality may persist at finite N. It is shown, in the half-BPS sector, that the states of D3 giant graviton branes in AdS5 × S5 are holographically dual to certain auxiliary ghosts that compensate for finite N trace relations in U(N) $$ \mathcal{N} $$ N = 4 super Yang-Mills. The complex formed from spaces of states of bulk D3 giants is observed to furnish a BRST-like resolution of the half-BPS Hilbert space of U(N) $$ \mathcal{N} $$ N = 4 SYM at finite N. We argue that the identification between the states of certain bulk D-branes and the auxiliary ghosts in the boundary holds rather generally at vanishing ’t Hooft coupling λ = 0. We propose that a complex, which furnishes a BRST-like resolution of the finite N Hilbert space of a boundary U(N) gauge theory at λ = 0, should be identified as the space of states of the dual string theory in the α′ → ∞ limit. The Lefschetz trace formula provides the holographic map in this regime, where bulk observables are computed by taking the alternating sum of the expectation values in an ensemble of states built on each open string vacuum. The giant graviton expansion is recovered and generalized in a limit of the resolution.

Section: Introductionmentioning

confidence: 95%

“…Giant gravitons are BPS branes on R × S m−2 ⊂ AdS n × S m that are supported via a large angular momentum induced from the background Ramond-Ramond potential [7,13,14]. See, for example, [11,[15][16][17][18][19][20][21][22][23][24][25][26] for related works.…”

Section: Introductionmentioning

confidence: 99%

Trace relations and open string vacua

Lee

2024

Self Cite

“…JHEP02(2023)109 Inspired by the recent discovery of the giant graviton expansion [65][66][67][68][69], we divide the finite-N BPS partition function (resp. index) by the infinite-N one, and plot the coefficients at each n in figure 2.…”

Section: Counting Data and A Giant-graviton-like Featurementioning

confidence: 99%

Words to describe a black hole

Chang

Lin

2023

We revamp the constructive enumeration of 1/16-BPS states in the maximally supersymmetric Yang-Mills in four dimensions, and search for ones that are not of multi-graviton form. A handful of such states are found for gauge group SU(2) at relatively high energies, resolving a decade-old enigma. Along the way, we clarify various subtleties in the literature, and prove a non-renormalization theorem about the exactness of the cohomological enumeration in perturbation theory. We point out a giant-graviton-like feature in our results, and envision that a deep analysis of our data will elucidate the fundamental properties of black hole microstates.

“…• We hope to report the detailed finite N and finite representation corrections and the giant graviton expansions of the Schur line defect correlators, as discussed for various supersymmetric indices in e.g. [65][66][67][68][69][70][71][72].…”

Section: Future Workmentioning

confidence: 99%

$$ \mathcal{N} $$ = 2* Schur indices

Hatsuda

Okazaki

2023

We find closed-form expressions for the Schur indices of 4d $$ \mathcal{N} $$ N = 2* super Yang-Mills theory with unitary gauge groups for arbitrary ranks via the Fermi-gas formulation. They can be written as a sum over the Young diagrams associated with spectral zeta functions of an ideal Fermi-gas system. These functions are expressed in terms of the twisted Weierstrass functions, generating functions for quasi-Jacobi forms. The indices lie in the polynomial ring generated by the Kronecker theta function and the Weierstrass functions which contains the polynomial ring of the quasi-Jacobi forms. The grand canonical ensemble allows for another simple exact form of the indices as infinite series. In addition, we find that the unflavored Schur indices and their limits can be expressed in terms of several generating functions for combinatorial objects, including sum of triangular numbers, generalized sums of divisors and overpartitions.