On highest-energy state in the su(1|1) sector of N=4 super Yang-Mills theory

We consider the highest-energy state in the su(1|1) sector of N=4 super Yang-Mills theory containing operators of the form tr(Z^{L-M} \psi^M) where Z is a complex scalar and \psi is a component of gaugino. We show that this state corresponds to the operator tr(\psi^L) and can be viewed as an analogue of the antiferromagnetic state in the su(2) sector. We find perturbative expansions of the energy of this state in both weak and strong 't Hooft coupling regimes using asymptotic gauge theory Bethe ansatz equations. We also discuss a possible analog of this state in the conjectured string Bethe ansatz equations.Comment: 23 pages, Late

Reduced sigma-model on AdS_5 x S^5: one-loop scattering amplitudes

We compute one-loop S-matrix in the reduced sigma-model which describes AdS_5 x S^5 string theory in the near-flat-space limit. The result agrees with the corresponding limit of the S-matrix in the full sigma-model, which demonstrates the consistency of the reduction at the quantum level.Comment: 9 pages, 1 figure; v2: reference added; v3: misprint in (3.6) corrected; v4: typo in (3.4) corrected; v5: new form of the actio

Aspects of Categorical Symmetries from Branes: SymTFTs and Generalized Charges

Recently it has been observed that branes in geometric engineering and holography have a striking connection with generalized global symmetries. In this paper we argue that branes, in a certain topological limit, not only furnish the symmetry generators, but also encode the so-called Symmetry Topological Field Theory (or SymTFT). For a $d$-dimensional QFT, this is a $(d+1)$-dimensional topological field theory, whose topological defects encode both the symmetry generators (invertible or non-invertible) and the generalized charges. Mathematically, the topological defects form the Drinfeld center of the symmetry category of the QFT. In this paper we derive the SymTFT and the Drinfeld center topological defects directly from branes. Central to the identification of these are Hanany-Witten brane configurations, which encode both topological couplings in the SymTFT and the generalized charges under the symmetries. We exemplify the general analysis with examples of QFTs realized in geometric engineering or holography.Comment: 68 pages plus appendice

5d superconformal field theories and graphs

We propose graphs, the Combined Fiber Diagrams (CFD), to characterize all 5d superconformal field theories (SCFTs) that arise as S1-reductions of 6d SCFTs. Transitions between CFDs encode mass deformations that trigger RG-flows between SCFTs. They provide a combinatorial classification of all such 5d SCFTs and encode physical information about the strongly coupled theories, like the superconformal flavor symmetry and BPS states. We consistently reproduce known results, but more importantly predict new theories and strong coupling effects in 5d SCFTs

Symmetry TFTs for 3d QFTs from M-theory

We derive the Symmetry Topological Field Theories (SymTFTs) for 3d supersymmetric quantum field theories (QFTs) constructed in M-theory either via geometric engineering or holography. These 4d SymTFTs encode the symmetry structures of the 3d QFTs, for instance the generalized global symmetries and their 't Hooft anomalies. Using differential cohomology, we derive the SymTFT by reducing M-theory on a 7-manifold $Y_7$, which either is the link of a conical Calabi-Yau four-fold or part of an $\text{AdS}_4\times Y_7$ holographic solution. In the holographic setting we first consider the 3d $\mathcal{N}=6$ ABJ(M) theories and derive the BF-couplings, which allow the identification of the global form of the gauge group, as well as 1-form symmetry anomalies. Secondly, we compute the SymTFT for 3d $\mathcal{N}=2$ quiver gauge theories whose holographic duals are based on Sasaki-Einstein 7-manifolds of type $Y_7 = Y^{p,k}(\mathbb{C}\mathbb{P}^2)$. The SymTFT encodes 0- and 1-form symmetries, as well as potential 't Hooft anomalies between these. Furthermore, by studying the gapped boundary conditions of the SymTFT we constrain the allowed choices for $U(1)$ Chern-Simons terms in the dual field theory.Comment: 44 pages plus appendice

A Panorama Of Physical Mathematics c. 2022

What follows is a broad-brush overview of the recent synergistic interactions between mathematics and theoretical physics of quantum field theory and string theory. The discussion is forward-looking, suggesting potentially useful and fruitful directions and problems, some old, some new, for further development of the subject. This paper is a much extended version of the Snowmass whitepaper on physical mathematics [1]

Two-loop AdS_5 x S^5 superstring: testing asymptotic Bethe ansatz and finite size corrections

We continue the investigation of two-loop string corrections to the energy of a folded string with a spin S in AdS_5 and an angular momentum J in S^5, in the scaling limit of large J and S with ell=pi J/(lambda^(1/2) ln S)=fixed. We compute the generalized scaling function at two-loop order f_2(ell) both for small and large values of ell matching the predictions based on the asymptotic Bethe ansatz. In particular, in the small ell expansion, we derive an exact integral form for the ell-dependent coefficient of the Catalan's constant term in f_2(ell). Also, by resumming a certain subclass of multi-loop Feynman diagrams we obtain an exact expression for the leading (ln ell) part of f(lambda^(1/2), ell) which is valid to any order in the alpha'~1/lambda^(1/2) expansion. At large ell the string energy has a BMN-like expansion and the first few leading coefficients are expected to be the same at weak and at strong coupling. We provide a new example of this non-renormalization for the term which is generated at two loops in string theory and at one-loop in gauge theory (sub-sub-leading in 1/J). We also derive a simple algebraic formula for the term of maximal transcendentality in f_2(ell) expanded at large ell. In the second part of the paper we initiate the study of 2-loop finite size corrections to the string energy by formally compactifying the spatial world-sheet direction in the string action expanded near long fast-spinning string. We observe that the leading finite-size corrections are of "Casimir" type coming from terms containing at least one massless propagator. We consider in detail the one-loop order (reproducing the leading Landau-Lifshitz model prediction) and then focus on the two-loop contributions to the (1/ln S) term (for J=0). We find that in a certain regularization scheme used to discard power divergences the two-loop coefficient of the (1/ln S) term appears to vanish.Comment: 50 pages, 4 figures v2: typos corrected, references adde

Infinite spin limit of semiclassical string states

Motivated by recent works of Hofman and Maldacena and Dorey we consider a special infinite spin limit of semiclassical spinning string states in AdS5 x S5. We discuss examples of known folded and circular 2-spin string solutions and demonstrate explicitly that the 1-loop superstring correction to the classical expression for the energy vanishes in the limit when one of the spins is much larger that the other. We also give a general discussion of this limit at the level of integral equations describing finite gap solutions of the string sigma model and argue that the corresponding asymptotic form of the string and gauge Bethe equations is the same.Comment: 38 pages, 3 figures; v2: comments on derivation of bound states of magnons from discrete Bethe equations added in section 4 and appendix C, references added, Imperial-TP-AT-6-4, HUTP-06/A002

Two-loop world-sheet corrections in AdS_5 x S^5 superstring

We initiate the computation of the 2-loop quantum AdS_5 x S^5 string corrections on the example of a certain string configuration in S^5 related by an analytic continuation to a folded rotating string in AdS_5 in the ``long string'' limit. The 2-loop term in the energy of the latter should represent the subleading strong-coupling correction to the cusp anomalous dimension and thus provide a further check of recent conjectures about the exact structure of the Bethe ansatz underlying the AdS/CFT duality. We use the conformal gauge and several choices of the \kappa-symmetry gauge. While we are unable to verify the cancellation of 2d UV divergences we compute the bosonic contribution to the effective action and also determine the non-trivial finite part of the fermionic contribution. Both the bosonic and the fermionic contributions to the string energy happen to be proportional to the Catalan's constant. The resulting value for 2-loop superstring prediction for the subleading coefficient a_2 in the scaling function matches the numerical value found in hep-th/0611135 from the BES equation.Comment: 48 pages, 1 Figure. v3: several mistakes corrected, the finite result for the 2-loop coefficient is found to agree with the numerical value found by Benna et al in hep-th/061113

On String S-matrix, Bound States and TBA

The study of finite J effects for the light-cone AdS superstring by means of the Thermodynamic Bethe Ansatz requires an understanding of a companion 2d theory which we call the mirror model. It is obtained from the original string model by the double Wick rotation. The S-matrices describing the scattering of physical excitations in the string and mirror models are related to each other by an analytic continuation. We show that the unitarity requirement for the mirror S-matrix fixes the S-matrices of both theories essentially uniquely. The resulting string S-matrix S(z_1,z_2) satisfies the generalized unitarity condition and, up to a scalar factor, is a meromorphic function on the elliptic curve associated to each variable z. The double Wick rotation is then accomplished by shifting the variables z by quarter of the imaginary period of the torus. We discuss the apparent bound states of the string and mirror models, and show that depending on a choice of the physical region there are one, two or 2^{M-1} solutions of the M-particle bound state equations sharing the same conserved charges. For very large but finite values of J, most of these solutions, however, exhibit various signs of pathological behavior. In particular, they might receive a finite J correction to their energy which is complex, or the energy correction might exceed corrections arising due to finite J modifications of the Bethe equations thus making the asymptotic Bethe ansatz inapplicable.Comment: 77 pages, 6 figures, v2: the statement about the periodicity condition for mirror fermions corrected; typos corrected; references added, v3: misprints correcte