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Results for “Supersymmetric gauge theory”

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DOE OSTI2020

Effective gravitational couplings of four-dimensional $ \mathcal{N} $ = 2 supersymmetric gauge theories

The low energy effective couplings of a four-dimensional N = 2 supersymmetric gauge theory to topological invariants of the background gravitational field are described by two functions A and B. These two functions play an important role in the study of topologically twisted four-dimensional N = 2 supersymmetric gauge theories and in the computation of central charges of N = 2 superconformal theories. In this paper, we compute A and B from the partition function in the Ω-background for SU(2) gauge theories. Our results not only confirm the predicted expressions of the effective gravitational couplings, but also give the previously undetermined overall multiplicative factors. We also analyze A and B for the SU(N) super-Yang-Mills theory, and confirm all the previous predictions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Infinite-dimensional fermionic symmetry in supersymmetric gauge theories

We establish the existence of an infinite-dimensional fermionic symmetry in four-dimensional supersymmetric gauge theories by analyzing semiclassical photino dynamics in abelian $\mathscr{N}$ = 1 theories with charged matter. The symmetry is parametrized by a spinor-valued function on an asymptotic S2 at null infinity. It is not manifest at the level of the Lagrangian, but acts non-trivially on physical states, and its Ward identity is the soft photino theorem. The infinite-dimensional fermionic symmetry resides in the same $\mathscr{N}$ = 1 supermultiplet as the physically non-trivial large gauge symmetries associated with the soft photon theorem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Trialities of minimally supersymmetric 2d gauge theories

We study dynamics of two-dimensional N = (0, 1) supersymmetric gauge theories. In particular, we propose that there is an infrared triality between certain triples of theories with orthogonal and symplectic gauge groups. The proposal is supported by matching of anomalies and elliptic genera. This triality can be viewed as a (0, 1) counterpart of the (0, 2) triality proposed earlier by two of the authors and A. Gadde. We also describe the relation between global anomalies in gauge theoretic and sigma-model descriptions, filling in a gap in the present literature.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Exact results in softly broken supersymmetric chiral gauge theories with flavor

We present exact results in softly broken supersymmetric SU⁡(𝑁 𝐶 ) chiral gauge theories with charged fermions in one antisymmetric, 𝑁 𝐹 fundamental, and 𝑁 𝐶 + 𝑁 𝐹 − 4 antifundamental representations. We achieve this by considering the supersymmetric version of these theories and utilizing anomaly mediated supersymmetry breaking at a scale 𝑚 ≪ Λ to generate a vacuum. The connection to nonsupersymmetric theories is then conjectured in the limit 𝑚 → ∞. For odd 𝑁 𝐶 , we determine the massless fermions and unbroken global symmetries in the infrared. For even 𝑁 𝐶 , we find global symmetries are nonanomalous and no massless fermions. In all cases, the symmetry breaking patterns differ from what the tumbling hypothesis would suggest.

Anomalies↗

DOE OSTI2024

Corners and islands in the S-matrix bootstrap of the open superstring

We bootstrap the Veneziano superstring amplitude in 10 dimensions from the bottom-up. Starting with the most general maximally supersymmetric Yang-Mills EFT, we input information about the lowest-lying massive states, which we assume contribute via tree-level exchanges to the 4-point amplitude. We show the following: (1) if there is only a single state at the lowest mass, it must be a scalar. (2) Assuming a string-inspired gap between the mass of this scalar and any other massive states, the allowed region of Wilson coefficients has a new sharp corner where the Veneziano amplitude is located. (3) Upon fixing the next massive state to be a vector, the EFT bounds have a one-parameter family of corners; these would correspond to models with linear Regge trajectories of varying slopes, one of which is the open superstring. (4) When the ratio between the massive scalar coupling and the tr F 4 coefficient is fixed to its string value, the spin and mass of the second massive state is determined by the bootstrap and the Veneziano amplitude is isolated on a small island in parameter space. Finally, we compare with other recent bootstraps approaches, both the pion model and imposing Regge-inspired maximal spin constraints.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

The superconformal index and black hole instabilities

The superconformal index of $\mathcal{N}$ = 4 supersymmetric Yang-Mills theory with gauge group U(N) has provided powerful insights into the entropy of supersymmetric black holes in AdS 5 × S 5 , including some sub-leading logarithmic and non-perturbative corrections. Recently, the phase space of supersymmetric solutions has been argued to contain configurations other than the asymptotically AdS 5 black hole. Such configurations include the so-called grey galaxies where the black hole at the center is surrounded by a gas of gravitons. By numerically evaluating the superconformal index of $\mathcal{N}$ = 4 supersymmetric Yang-Mills at small values of N, we detect systematic deviations from the entropy of black holes with two distinct angular momenta. We find that the giant graviton expansion of the index is a numerically efficient way of evaluating the index that complements the direct character evaluation and allows for explicit access to N ≤ 15 with up to two giant gravitons in the expansion. We find it remarkable that a supersymmetric quantity in field theory, usually thought of as a rigid counting observable, indeed contains information about different phases in the space of supersymmetric solutions on the gravity side.

AdS-CFT correspondence↗

DOE OSTI2020

A note on chiral trace relations from qq-characters

We study chiral operators in four-dimensional N = 2 supersymmetric gauge theories. We provide a general procedure to derive the exact relations among the vacuum expectation values of chiral operators in the Ω-background using the non-perturbative Dyson-Schwinger equations of qq-characters. We demonstrate our procedure using several examples. For pure SU(N) gauge theory and SU(N) gauge theory with 2N fundamental hypermultiplets, we verify the relations conjectured previously in the literature. We also briefly discuss the relations in SU(N) linear superconformal quiver gauge theories.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Riemann-Hilbert correspondence and blown up surface defects

The relationship of two dimensional quantum field theory and isomonodromic deformations of Fuchsian systems has a long history. Recently four-dimensional N = 2 gauge theories joined the party in a multitude of roles. In this paper we study the vacuum expectation values of intersecting half-BPS surface defects in SU(2) theory with N f = 4 fundamental hypermultiplets. We show they form a horizontal section of a Fuchsian system on a sphere with 5 regular singularities, calculate the monodromy, and define the associated isomonodromic tau-function. Using the blowup formula in the presence of half-BPS surface defects, initiated in the companion paper, we obtain the GIL formula, establishing an unexpected relation of the topological string/free fermion regime of supersymmetric gauge theory to classical integrability.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Loop equation and exact soft anomalous dimension in $ \mathcal{N} $ = 4 super Yang-Mills

BPS Wilson loops in supersymmetric gauge theories have been the subjects of active research since they are often amenable to exact computation. So far most of the studies have focused on loops that do not intersect. In this paper, we derive exact results for intersecting 1/8 BPS Wilson loops in $ \mathcal{N} $ = 4 supersymmetric Yang-Mills theory, using a combination of supersymmetric localization and the loop equation in 2d gauge theory. The result is given by a novel matrix-model-like representation which couples multiple contour integrals and a Gaussian matrix model. We evaluate the integral at large N, and make contact with the string worldsheet description at strong coupling. As an application of our results, we compute exactly a small-angle limit (and more generally near-BPS limits) of the cross anomalous dimension which governs the UV divergence of intersecting Wilson lines. The same quantity describes the soft anomalous dimension of scattering amplitudes of W-bosons in the Coulomb branch.

't Hooftand Polyakov loops↗

DOE OSTI2025

Generalized symmetry constraints on deformed 4D SCFTs

We explore the consequence of generalized symmetries in four-dimensional N = 1 superconformal field theories. First, we classify all possible supersymmetric gauge theories with a simple gauge group that have a nontrivial one-form symmetry and flows to a superconformal field theory. Upon identifying unbroken discrete zero-form symmetries from the Adler-Bell-Jackiw (ABJ) anomaly, we find that many of these theories have mixed zero-form or one-form ’t Hooft anomalies. Then we classify the relevant deformations of these SCFTs that preserve the anomaly. From this mixed anomaly together with the anomalies of the discrete zero-form symmetries, we find obstructions for the relevant deformations of these SCFTs to flow to a trivially gapped phase. We also study non-Lagrangian SCFTs formed by gauging copies of Argyres-Douglas theories and constrain their deformations. In particular, we explore a new duality between the diagonal gauging of two D 3 ( S U ( N ) ) theories and S U ( N ) gauge theory with two adjoints. We also repeat our analysis for a host of nonsupersymmetric gauge theories having nontrivial one-form symmetry including examples that appear to flow to Bank-Zaks type CFTs. Published by the American Physical Society 2025

Kang, Monica Jinwoo (ORCID:0000000204542064)↗

DOE OSTI2021

Sub-leading structures in superconformal indices: subdominant saddles and logarithmic contributions

We systematically study various sub-leading structures in the superconformal index of N = 4 supersymmetric Yang-Mills theory with SU(N) gauge group. We concentrate in the superconformal index description as a matrix model of elliptic gamma functions and in the Bethe-Ansatz presentation. Our saddle-point approximation goes beyond the Cardy-like limit and we uncover various saddles governed by a matrix model corresponding to SU(N) Chern-Simons theory. The dominant saddle, however, leads to perfect agreement with the Bethe-Ansatz approach. We also determine the logarithmic correction to the superconformal index to be log N, finding precise agreement between the saddle-point and Bethe-Ansatz approaches in their respective approximations. We generalize the two approaches to cover a large class of 4d N = 1 superconformal theories. We find that also in this case both approximations agree all the way down to a universal contribution of the form log N. The universality of this last result constitutes a robust signature of this ultraviolet description of asymptotically AdS 5 black holes and could be tested by low-energy IIB supergravity.

1/N expansion↗

DOE OSTI2020

“Lagrangian disks” in M-theory

While the study of bordered (pseudo-)holomorphic curves with boundary on Lagrangian submanifolds has a long history, a similar problem that involves (special) Lagrangian submanifolds with boundary on complex surfaces appears to be largely overlooked in both physics and math literature. We relate this problem to geometry of coassociative submanifolds in G 2 holonomy spaces and to Spin(7) metrics on 8-manifolds with T 2 fibrations. As an application to physics, we propose a large class of brane models in type IIA string theory that generalize brane brick models on the one hand and 2d theories T[M 4 ] on the other.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Navigating collinear superspace

We introduce a new set of effective field theory rules for constructing Lagrangians with $ \mathcal{N} $ = 1 supersymmetry in collinear superspace. In the standard superspace treatment, superfields are functions of the coordinates $ \left({x}^{\mu },{\theta}^{\alpha },{\theta}^{\dagger \overset{\cdot }{\alpha }}\right) $ , and supersymmetry preservation is manifest at the Lagrangian level in part due to the inclusion of auxiliary F - and D -term components. By contrast, collinear superspace depends on a smaller set of coordinates ( x μ , η , η † ), where η is a complex Grassmann number without a spinor index. This provides a formulation of supersymmetric theories that depends exclusively on propagating degrees of freedom, at the expense of obscuring Lorentz invariance and introducing inverse momentum scales. After establishing the general framework, we construct collinear superspace Lagrangians for free chiral matter and non-Abelian gauge fields. For the latter construction, an important ingredient is a superfield representation that is simultaneously chiral, anti-chiral, and real; this novel object encodes residual gauge transformations on the light cone. Additionally, we discuss a fundamental obstruction to constructing inter- acting theories with chiral matter; overcoming these issues is the subject of our companion paper, where we introduce a larger set of superfields to realize the full range of interactions compatible with $ \mathcal{N} $ = 1. Along the way, we provide a novel framing of reparametrization invariance using a spinor decomposition, which provides insight into this important light-cone symmetry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

N = 8 Supergravity from Positivity

The duality between color and kinematics brings many simplifications to the construction of scattering amplitudes. Here, we show that satisfaction of the tree-level Bern-Carrasco-Johansson relations can dramatically simplify loop computations even when the loop-level relations are not explicitly satisfied. We introduce an agglomerative algorithm, color-dual cut tiling, that builds the entire integrand from the simplest on-shell conditions applied to a seed of off-shell integrand information. Specifically, we demonstrate that for two-to-two scattering at three loops in the maximally supersymmetric gauge theory there is sufficient information contained in planar cuts—completely determined by positivity constraints—to generate all of the nonplanar sector. We further make use of the generalized double copy to generate a representation of maximally supersymmetric gravity as a functional of the planar SYM input. We close with comments on generalizations and possible applications of the approach. Published by the American Physical Society 2025

Carrasco, John Joseph M. (ORCID:0000000244998488)↗

DOE OSTI2023

Cardy expansion of 3d superconformal indices and corrections to the dual black hole entropy

We consider the superconformal index of three-dimensional $\mathcal{N}$ = 2 supersymmetric field theories computed via localization on S 1 × S 2 . We systematically develop an expansion where the ratio of the radius of S 1 to the radius of S 2 is taken very small — a Cardy-like expansion. We emphasize the sub-leading structures in this Cardy-like expansion as well as their interplay with the large-N limit for theories with gauge group of the form product of U(N) factors. We demonstrate that taking the large-N limit first leads to an expression for the effective action yielding the index that only includes terms proportional to 1/β and powers of β i=0,1,2 where β is the ratio of radii. As we depart from the β → 0 limit for finite N, we find indications of non-perturbative contributions of the form e –1/β . We present an explicit evaluation of the superconformal index for the ABJM theory in the large-N limit that is exact in β up to non-perturbative corrections. For the ABJM theory we explore the implications of the Cardy-like expansion for corrections to the entropy of the rotating, electricallly charged, asymptotically AdS 4 dual black hole. Interestingly, we find a closed form for the entropy that includes all perturbative corrections in β and takes the form of the leading order expression but with shifted charges.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Subleading corrections to the S 3 free energy of necklace quiver theories dual to massive IIA

We investigate the S 3 free energy of N = 3 Chern-Simons-matter quiver gauge theories with gauge group U(N) r (r ≥ 2) where the sum of Chern-Simons levels does not vanish, beyond the leading order in the large-N limit. We take two different approaches to explore the sub-leading structures of the free energy. First we evaluate the matrix integral for the partition function in the ’t Hooft limit using a saddle point approximation. Second we use an ideal Fermi-gas model to compute the same partition function, but in the limit of fixed Chern-Simons levels. The resulting expressions for the free energy F = – log Z are then compared in the overlapping parameter regime. The Fermi-gas approach also hints at a universal 1/6 log N correction to the free energy. Since the quiver gauge theories we consider are dual to massive Type IIA theory, we expect the sub-leading correction of the planar free energy in the large ’t Hooft parameter limit to match higher-derivative corrections to the tree-level holographic dual free energy, which have not yet been fully investigated.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Microstate counting via Bethe Ansätze in the 4d $ \mathcal{N} $ = 1 superconformal index

We study the superconfomal index of four-dimensional toric quiver gauge theories using a Bethe Ansatz approach recently applied by Benini and Milan. Relying on a particular set of solutions to the corresponding Bethe Ansatz equations we evaluate the superconformal index in the large N limit, thus avoiding to take any Cardy-like limit. We present explicit results for theories arising as a stack of N D 3 branes at the tip of toric Calabi-Yau cones: the conifold theory, the suspended pinch point gauge theory, the first del Pezzo theory and Y p,q quiver gauge theories. For a suitable choice of the chemical potentials of the theory we find agreement with predictions made for the same theories in the Cardy-like limit. However, for other regions of the domain of chemical potentials the superconformal index is modified and consequently the associated black hole entropy receives corrections. We work out explicitly the simple case of the conifold theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Subleading corrections to the free energy in a theory with N 5/3 scaling

We numerically investigate the sphere partition function of a Chern-Simons-matter theory with SU(N) gauge group at level k coupled to three adjoint chiral multiplets that is dual to massive IIA theory. Beyond the leading order N 5/3 behavior of the free energy, we find numerical evidence for a term of the form (2/9) log N. We conjecture that this term may be universal in theories with N 5/3 scaling in the large-N limit with the Chern-Simons level k held fixed.

1/N Expansion↗