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Register a new userThe Weak Coupling Spectrum around Isolated Vacua in N=4 Super Yang-Mills on T^3 with any Gauge Group
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The moduli space of flat connections for maximally supersymmetric Yang-Mills theories, in a space-time of the form T^3xR, contains isolated points, corresponding to normalizable zero energy states, for certain simple gauge groups G. We consider the low energy effective field theories in the weak coupling limit supported on such isolated points and find that when quantized they consist of an infinite set of harmonic oscillators whose angular frequencies are completely determined by the Lie algebra of G. We then proceed to find the isolated flat connections for all simple G and subsequently specify the corresponding effective field theories.
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We study the question of existence and the number of normalized vacuum states in N = 4 super-Yang-Mills quantum mechanics for any gauge group. The mass deformation method is the simplest and clearest one. It allowed us to calculate the number of normalized vacuum states for all gauge groups. For all unitary groups, #(vac) = 1, but for the symplectic groups [starting from Sp(6) ], for the orthogonal groups [starting from SO(8)] and for all the exceptional groups, it is greater than one. We also discuss at length the functional integral method. We calculate the ``deficit term for some non-unitary groups and predict the value of the integral giving the ``principal contribution. The issues like the Born-Oppenheimer procedure to derive the effective theory and the manifestation of the localized vacua for the asymptotic effective wave functions are also discussed.
We consider the pure supersymmetric Yang--Mills theories placed on a small 3-dimensional spatial torus with higher orthogonal and exceptional gauge groups. The problem of constructing the quantum vacuum states is reduced to a pure mathematical problem of classifying the flat connections on 3-torus. The latter problem is equivalent to the problem of classification of commuting triples of elements in a connected simply connected compact Lie group which is solved in this paper. In particular, we show that for higher orthogonal SO(N), N > 6, and for all exceptional groups the moduli space of flat connections involves several distinct connected components. The total number of vacuumstates is given in all cases by the dual Coxeter number of the group which agrees with the result obtained earlier with the instanton technique.
We consider N = 4 Yang-Mills theory on a flat four-torus with the R-symmetry current coupled to a flat background connection. The partition function depends on the coupling constant of the theory, but when it is expanded in a power series in the R-symmetry connection around the loci at which one of the supersymmetries is unbroken, the constant and linear terms are in fact independent of the coupling constant and can be computed at weak coupling for all non-trivial t Hooft fluxes. The case of a trivial t Hooft flux is difficult because of infrared problems, but the corresponding terms in the partition function are uniquely determined by S-duality.
We study event shapes in N=4 SYM describing the angular distribution of energy and R-charge in the final states created by the simplest half-BPS scalar operator. Applying the approach developed in the companion paper arXiv:1309.0769, we compute these observables using the correlation functions of certain components of the N=4 stress-tensor supermultiplet: the half-BPS operator itself, the R-symmetry current and the stress tensor. We present master formulas for the all-order event shapes as convolutions of the Mellin amplitude defining the correlation function of the half-BPS operators, with a coupling-independent kernel determined by the choice of the observable. We find remarkably simple relations between various event shapes following from N=4 superconformal symmetry. We perform thorough checks at leading order in the weak coupling expansion and show perfect agreement with the conventional calculations based on amplitude techniques. We extend our results to strong coupling using the correlation function of half-BPS operators obtained from the AdS/CFT correspondence.
We consider the ambitwistor description of $mathcal N$=4 supersymmetric extension of U($N$) Yang-Mills theory on Minkowski space $mathbb R^{3,1}$. It is shown that solutions of super-Yang-Mills equations are encoded in real-analytic U($N$)-valued functions on a domain in superambitwistor space ${mathcal L}_{mathbb R}^{5|6}$ of real dimension $(5|6)$. This leads to a procedure for generating solutions of super-Yang-Mills equations on $mathbb R^{3,1}$ via solving a Riemann-Hilbert-type factorization problem on two-spheres in $mathcal L_{mathbb R}^{5|6}$.
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