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Register a new userOn highest-energy state in the su(1|1) sector of N=4 super Yang-Mills theory
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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.
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We study the multiplicity of BPS domain walls in N=1 super Yang-Mills theory, by passing to a weakly coupled Higgs phase through the addition of fundamental matter. The number of domain walls connecting two specified vacuum states is then determined via the Witten index of the induced worldvolume theory, which is invariant under the deformation to the Higgs phase. The worldvolume theory is a sigma model with a Grassmanian target space which arises as the coset associated with the global symmetries broken by the wall solution. Imposing a suitable infrared regulator, the result is found to agree with recent work of Acharya and Vafa in which the walls were realized as wrapped D4-branes in IIA string theory.
We present a formulation of N=(1,1) super Yang-Mills theory in 1+1 dimensions at finite temperature. The partition function is constructed by finding a numerical approximation to the entire spectrum. We solve numerically for the spectrum using Supersymmetric Discrete Light-Cone Quantization (SDLCQ) in the large-N_c approximation and calculate the density of states. We find that the density of states grows exponentially and the theory has a Hagedorn temperature, which we extract. We find that the Hagedorn temperature at infinite resolution is slightly less than one in units of (g^(2) N_c/pi)^(1/2). We use the density of states to also calculate a standard set of thermodynamic functions below the Hagedorn temperature. In this temperature range, we find that the thermodynamics is dominated by the massless states of the theory.
This paper concerns a special class of $n$-point correlation functions of operators in the stress tensor supermultiplet of $mathcal{N}=4$ supersymmetric $SU(N)$ Yang-Mills theory. These are maximal $U(1)_Y$-violating correlators that violate the bonus $U(1)_Y$ charge by a maximum of $2(n-4)$ units. We will demonstrate that such correlators satisfy $SL(2,mathbb{Z})$-covariant recursion relations that relate $n$-point correlators to $(n-1)$-point correlators in a manner analogous to the soft dilaton relations that relate the corresponding amplitudes in flat-space type IIB superstring theory. These recursion relations are used to determine terms in the large-$N$ expansion of $n$-point maximal $U(1)_Y$-violating correlators in the chiral sector, including correlators with four superconformal stress tensor primaries and $(n-4)$ chiral Lagrangian operators, starting from known properties of the $n=4$ case. We concentrate on the first three orders in $1/N$ beyond the supergravity limit. The Mellin representations of the correlators are polynomials in Mellin variables, which correspond to higher derivative contact terms in the low-energy expansion of type IIB superstring theory in $AdS_5 times S^5$ at the same orders as $R^4, d^4R^4$ and $d^6R^4$. The coupling constant dependence of these terms is found to be described by non-holomorphic modular forms with holomorphic and anti-holomorphic weights $(n-4,4-n)$ that are $SL(2, mathbb{Z})$-covariant derivatives of Eisenstein series and certain generalisations. This determines a number of non-leading contributions to $U(1)_Y$-violating $n$-particle interactions ($n>4$) in the low-energy expansion of type IIB superstring amplitudes in $AdS_5times S^5$.
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 use fractional and wrapped branes to describe perturbative and non-perturbative properties of N=1 super Yang-Mills living on their world-volume. (Talk given at the 1st Nordstrom Symposium, Helsinki, August 2003.)
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