We consider D-branes in the Dabholkar-Park (DP) background, a 9d orientifold theory obtained by gauging symmetry in the type IIB string theory compactified on a circle. Using anomalies in the world-sheet theory, we provide physical insights into the classification of stable D-branes by relative KR-theory. The nature, such as stability, of D-branes wrapping along the compactified circle can be extracted from information about 1d Majorana fermions on the boundary of the world-sheet. These Majorana fermions need to be introduced to consistently perform the GSO projection and the orientifold. We also construct D-brane states in the DP background. The spectrum of D-branes characterized by the relative KR-theory is correctly reproduced from the D-brane states.

Japan

Hiroki Wada

Satoshi Yamaguchi

Anomalies and D-branes in the Dabholkar-Park background

South Korea

Sunjin Choi

Seok Kim

Eunwoo Lee

United States

Siyul Lee

Jaemo Park

Erratum to: Towards quantum black hole microstates

The BPS spectrum of AdS/CFT exhibits multi-gravitons at low energies, while having black hole states at higher energies. This can be studied concretely in AdS5/CFT4 in terms of classical cohomologies, even in the quantum regimes at finite 1/N. Recently, Chang and Lin found a threshold for non-graviton states in the SU(2) maximal super-Yang-Mills theory. We explicitly construct and present this threshold cohomology.

The shape of non-graviton operators for SU(2)

We study the cohomology of local BPS operators in $$ \mathcal{N} $$ = 4 Yang-Mills theory. The finite cohomologies consist of the graviton part (subject to the stringy exclusion principle) and the rest which may describe black hole microstates in quantum AdS/CFT. We construct an infinite tower of non-graviton cohomologies in the SU(2) theory and study to what extent they simulate quantum black holes. We find signals for partial no-hair behaviors by showing that certain gravitons are forbidden to dress these cohomologies. This is in qualitative agreement with the perturbative hairs allowed around black holes, which also leads us to a natural setup to construct hairy BPS black holes. The cohomologies are simpler to study in the BMN matrix model truncation of the classical field theory.

Towards quantum black hole microstates

We propose new 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 Seiberg-like dualities by considering various monopole superpotential deformations on 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 U(N  c ) SQCDs with fundamental and adjoint matter fields. We provide nontrivial evidence of these new dualities by comparing the superconformal indices, from which we analyze the change of the moduli space due to the monopole deformation. In addition, we perform the F-maximization to check the relevance of the monopole deformation for some examples, one of which is found to exhibit nontrivial symmetry enhancement in the IR. We prove such enhancement of the global symmetry using the superconformal index.

United Kingdom

Chiung Hwang

Sungjoon Kim

Monopole deformations of 3d Seiberg-like dualities with adjoint matters

According to the covariant open superstring description of 1/2-BPS D-branes in the AdS5×S5 background, there are two kinds of purely instantonic D-branes. One is the well known D(-1)-brane or D-instanton, and another is the D1-brane spanning a two dimensional subspace inside S5. We identify the actual 1/2-BPS instantonic D1-brane configurations and their supersymmetry structures. From the results, it is concluded that any spherical D1-instanton with the radius equal to that of S5 is 1/2-BPS. After evaluating the 1/2-BPS D1-instanton action, we discuss the relation of D1-instanton with the (p, q) string instanton. We also discuss the possible 1/2-BPS and 1/4-BPS multiple D1-instanton configurations.

Hyeonjoon Shin

Supersymmetric instantonic D1-branes in AdS5 ×S5 background

We propose new ADHM-like methods to compute the Coulomb branch instanton partition functions of 5D and 6D supersymmetric gauge theories, with certain exceptional gauge groups or exceptional matters. We study <math><msub><mi>G</mi><mn>2</mn></msub></math> theories with <math><msub><mi>n</mi><mn>7</mn></msub><mo>≤</mo><mn>3</mn></math> matters in <math><mrow><mn>7</mn></mrow></math> and <math><mi>S</mi><mi>O</mi><mo>(</mo><mn>7</mn><mo>)</mo></math> theories with <math><msub><mi>n</mi><mn>8</mn></msub><mo>≤</mo><mn>4</mn></math> matters in the spinor representation <math><mrow><mn>8</mn></mrow></math>. We also study the elliptic genera of self-dual instanton strings of 6D SCFTs with exceptional gauge groups or matters, including all non-Higgsable atomic SCFTs with rank 2 or 3 tensor branches. Some of them are tested with topological vertex calculus. We also explore a D-brane-based method to study instanton particles of 5D <math><mi>S</mi><mi>O</mi><mo>(</mo><mn>7</mn><mo>)</mo></math> and <math><mi>S</mi><mi>O</mi><mo>(</mo><mn>8</mn><mo>)</mo></math> gauge theories with matters in spinor representations, which further tests our ADHM-like proposals.

Hee-Cheol Kim

Joonho Kim

Ki-Hong Lee

6D strings and exceptional instantons

According to the covariant open superstring description of D-branes in the <math><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>×</mo><msup><mrow><mi>CP</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></math> background, <math><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math>-BPS D2-branes are purely instantonic. Based on this and by taking the eleven dimensional viewpoint, we identify the <math><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math>-BPS instantonic M2-brane configurations in the <math><mrow><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>×</mo></mrow><msup><mrow><mi>S</mi></mrow><mrow><mn>7</mn></mrow></msup><mo>/</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>k</mi></mrow></msub></mrow></math> background, which reduces to the <math><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>×</mo><msup><mi>CP</mi><mn>3</mn></msup></mrow></math> under the large <math><mi>k</mi></math> limit, and evaluate their action values. We also consider the previously known <math><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math>-BPS instantonic objects in ten dimensions from the M2-brane viewpoint to compare with our results.

<math><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math>-BPS membrane instantons in <math><mrow><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>×</mo></mrow><msup><mrow><mi>S</mi></mrow><mrow><mn>7</mn></mrow></msup><mo>/</mo><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>k</mi></mrow></msub></mrow></mrow></math>

We consider the analogue of Seiberg duality for two-dimensional   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = (2, 2) gauge theory with orthogonal gauge groups and with fundamental chiral multiplets proposed by Hori. Following Hori, when we consider O(k) gauge group as the (semi)-direct product of SO(k) ⋉ Z 2, we have to consider two kinds of the theories O±(k) depending on the orbifold action of Z 2. We give the evidences for the proposed dualities by working out the elliptic genus of dual pair. The matching of the elliptic genus is worked out perfectly for the proposed dualities.

Hyungchul Kim

2D Seiberg-like dualities for orthogonal gauge groups

We study the elliptic genera of 6d strings based on their modular properties. They are weak Jacobi forms of weight 0, whose indices are determined from the 2d chiral anomalies. We propose the ansatz for the elliptic genera which reflects the analytic structure of instanton partition functions. Given a finite amount of initial BPS data, we completely determine the elliptic genera of 6d strings in various 6d SCFTs. We also apply our ansatz to study   <math> <mi>N</mi> <mo>=</mo> <mfenced> <mn>2</mn> <mn>0</mn> </mfenced> </math>  $$ \mathcal{N}=\left(2,0\right) $$  and (1, 1) little strings as well as   <math> <mi>N</mi> <mo>=</mo> <mfenced> <mn>1</mn> <mn>0</mn> </mfenced> </math>  $$ \mathcal{N}=\left(1,0\right) $$  heterotic little strings, for which T-duality of little string theories supplies a sufficient number of initial BPS data. The anomaly polynomials of 6d little strings are worked out, which is needed for the elliptic genera bootstrap. In some little string theories, the elliptic genera must have the extra contributions from the Coulomb branch, which correspond to the additional zero modes for the full strings. The modified ansatze for such elliptic genera are also discussed.