Supersymmetric states of đť’© = 4 Yang-Mills from giant gravitons (original) (raw)
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Nuclear Physics B, 1998
We discuss the spectrum of states of IIB supergravity on AdS 5 Ă— S 5 in a manifest SU (2, 2/4) invariant setting. The boundary fields are described in terms of N = 4 superconformal Yang-Mills theory and the proposed correspondence between supergravity in AdS 5 and superconformal invariant singleton theory at the boundary is formulated in an N = 4 superfield covariant language.
Quantum space-times and finite effects in 4D super Yang–Mills theories
Nuclear Physics B, 2000
The truncation in the number of single-trace chiral primary operators of N = 4 SYM and its conjectured connection with gravity on quantum spacetimes are elaborated. The model of quantum spacetime we use is AdS 5 q Ă—S 5 q for q a root of unity. The quantum sphere is defined as a homogeneous space with manifest SU q (3) symmetry, but as anticipated from the field theory correspondence, we show that there is a hidden SO q (6) symmetry in the constrution. We also study some properties of quantum space quotients as candidate models for the quantum spacetime relevant for some Z n quiver quotients of the N = 4 theory which break SUSY to N = 2. We find various qualitative agreements between the proposed models and the properties of the corresponding finite N gauge theories.
M5-Branes, D4-Branes and quantum 5D super-Yang-Mills
2011
We revisit the relation of the six-dimensional (2, 0) M5-brane Conformal Field Theory compactified on S 1 to 5D maximally supersymmetric Yang-Mills Gauge Theory. We show that in the broken phase 5D super-Yang-Mills contains a spectrum of soliton states that can be identified with the complete Kaluza-Klein modes of an M2-brane ending on the M5-branes. This provides evidence that the (2, 0) theory on S 1 is equivalent to 5D super-Yang-Mills with no additional UV degrees of freedom, suggesting that the latter is in fact a well-defined quantum theory and possibly finite.
Massive super-Yang–Mills quantum mechanics: Classification and the relation to supermembrane
Nuclear Physics B, 2006
We classify the supersymmetric mass deformations of all the super Yang-Mills quantum mechanics, which are obtained by dimensional reductions of minimal super Yang-Mills in spacetime dimensions: ten, six, four, three and two. The resulting actions can be viewed as the matrix descriptions of supermembranes in nontrivial backgrounds of one higher dimensional supergravity theories. We also discuss the utmost generalization of the light-cone formulation of the Nambu-Goto action for a p-brane, including time dependent backgrounds.
Rings of short đť’© = 3 superfields in three dimensions and M-theory on AdS 4 Ă— N 0,1,0
Classical and Quantum Gravity, 2001
In this paper we investigate three-dimensional superconformal gauge theories with N = 3 supersymmetry. Independently from specific models, we derive the shortening conditions for unitary representations of the Osp(3|4) superalgebra and we express them in terms of differential constraints on three dimensional N = 3 superfields. We find a ring structure underlying these short representations, which is just the direct generalization of the chiral ring structure of N = 2 theories. When the superconformal field theory is realized on the world-volume of an M2-brane such superfield ring is the counterpart of the ring defined by the algebraic geometry of the 8-dimensional cone transverse to the brane. This and other arguments identify the N = 3 superconformal field theory dual to M-theory compactified on AdS 4 Ă— N 0,1,0. It is an N = 3 gauge theory with SU(N) Ă— SU(N) gauge group coupled to a suitable set of hypermultiplets, with an additional Chern Simons interaction. The AdS/CFT correspondence can be directly verified using the recently worked out Kaluza Klein spectrum of N 0,1,0 and we find a perfect match. We also note that besides the usual set of BPS conformal operators dual to the lightest KK states, we find that the composite operators corresponding to certain massive KK modes are organized into a massive spin 3 2 N = 3 multiplet that might be identified with the super-Higgs multiplet of a spontaneously broken N = 4 theory. We investigate this intriguing and inspiring feature in a separate paper.
Quantum states to brane geometries via fuzzy moduli spaces of giant gravitons
Journal of High Energy Physics, 2012
Eighth-BPS local operators in N = 4 SYM are dual to quantum states arising from the quantization of a moduli space of giant gravitons in AdS 5 Ă— S 5. Earlier results on the quantization of this moduli space give a Hilbert space of multiple harmonic oscillators in 3 dimensions. We use these results, along with techniques from fuzzy geometry, to develop a map between quantum states and brane geometries. In particular there is a map between the oscillator states and points in a discretization of the base space in the toric fibration of the moduli space. We obtain a geometrical decomposition of the space of BPS states with labels consisting of U (3) representations along with U (N) Young diagrams and associated group theoretic multiplicities. Factorization properties in the counting of BPS states lead to predictions for BPS world-volume excitations of specific brane geometries. Some of our results suggest an intriguing complementarity between localisation in the moduli space of branes and localisation in space-time.
Rings of short= 3 superfields in three dimensions and M-theory on AdS4Ă— N0, 1, 0
In this paper we investigate three-dimensional superconformal gauge theories with N = 3 supersymmetry. Independently from specific models, we derive the shortening conditions for unitary representations of the Osp(3|4) superalgebra and we express them in terms of differential constraints on three dimensional N = 3 superfields. We find a ring structure underlying these short representations, which is just the direct generalization of the chiral ring structure of N = 2 theories. When the superconformal field theory is realized on the world-volume of an M2-brane such superfield ring is the counterpart of the ring defined by the algebraic geometry of the 8-dimensional cone transverse to the brane. This and other arguments identify the N = 3 superconformal field theory dual to M-theory compactified on AdS 4 Ă— N 0,1,0 . It is an N = 3 gauge theory with SU(N) Ă— SU(N) gauge group coupled to a suitable set of hypermultiplets, with an additional Chern Simons interaction. The AdS/CFT correspondence can be directly verified using the recently worked out Kaluza Klein spectrum of N 0,1,0 and we find a perfect match. We also note that besides the usual set of BPS conformal operators dual to the lightest KK states, we find that the composite operators corresponding to certain massive KK modes are organized into a massive spin 3 2 N = 3 multiplet that might be identified with the super-Higgs multiplet of a spontaneously broken N = 4 theory. We investigate this intriguing and inspiring feature in a separate paper.
On The Super Five Brane Hamiltonian
The explicit form of the Wess-Zumino term of the PST super 5-brane Lagrangian in 11 dimensions is obtained. A complete canonical analysis for a gauge fixed PST super 5-brane action reveals the expected mixture of first and second class constraints and a canonical Hamiltonian that is quadratic in the antisymmetric gauge field. Finally, we find the light cone gauge Hamiltonian for the theory and comment on its stability properties.
Physical Review D, 2001
We apply supersymmetric discrete light-cone quantization (SDLCQ) to the study of supersymmetric Yang-Mills theory on R Ă— S 1 Ă— S 1. One of the compact directions is chosen to be light-like and the other to be space-like. Since the SDLCQ regularization explicitly preserves supersymmetry, this theory is totally finite, and thus we can solve for bound-state wave functions and masses numerically without renormalizing. We present an overview of all the massive states of this theory, and we see that the spectrum divides into two distinct and disjoint sectors. In one sector the SDLCQ approximation is only valid up to intermediate coupling. There we find a well defined and well behaved set of states, and we present a detailed analysis of these states and their properties. In the other sector, which contains a completely different set of states, we present a much more limited analysis for strong coupling only. We find that, while these state have a well defined spectrum, their masses grow with the transverse momentum cutoff. We present an overview of these states and their properties.
Solving four-dimensional field theories with the Dirichlet fivebrane
Physical Review D, 1999
The realization of N = 2 four dimensional super Yang-Mills theories in terms of a single Dirichlet fivebrane in type IIB string theory is considered. A classical brane computation reproduces the full quantum low energy effective action. This result has a simple explanation in terms of mirror symmetry. A particularly fruitful approach to the study of supersymmetric quantum field theories has been to realize these theories as a limit of string or M theory where gravitational effects decouple. There are two complementary approaches to this problem-the geometric engineering [1] approach and the Hanany-Witten brane set up [2]. To study N = 2 super Yang-Mills theories in 3 + 1 dimensions within the geometric engineering approach, one typically compactifies type IIA/B string theory on a Calabi-Yau threefold. The full non-perturbative solution of the N = 2 super Yang-Mills theory is then obtained by invoking mirror symmetry. In the Hanany-Witten approach, one typically considers a web of branes in a flat space. In order to study N = 2 super Yang-Mills theory in 3 + 1 dimensions, one considers two parallel solitonic fivebranes with a number of Dirichlet fourbranes stretched between them [3]. In this approach, all perturbative and non-perturbative corrections to the field theory are coded into the shape of the branes. The solution of these theories is performed by lifting to M theory. After the lift, the original type IIA brane set up is reinterpreted as a single fivebrane in M theory, wrapping the Seiberg-Witten curve Σ. The relationship between these two approaches has been explained in [4]. In this report, we will study N = 2 super Yang-Mills theory using the Hanany-Witten approach. Up to now, the description of the M theory fivebrane relevant for N = 2 super Yang-Mills theory has been in terms of eleven dimensional supergravity, which is a valid description of M theory at low energy [5]. A number of holomorphic quantities [6] including the exact low energy effective action [5] can be recovered using the supergravity description. The supergravity description corresponds to a strong coupling description of the original type IIA setup. However, one expects the field theory to emerge in the opposite limit, where the string theory is weakly coupled [7]. This limit is not captured by the supergravity approximation, so that one expects that the supergravity approach will only be capable of reproducing field theory quantities which are protected by supersymmetry. In this note, we will provide a direct construction in string theory which realizes the N = 2 super Yang-Mills theory in terms of a single Dirichlet fivebrane wrapping the Seiberg-Witten curve. We will be mainly concerned with two important issues: how a matrix description is obtained and how the string theory configurations described in this article are related to the original type IIA brane set up [3]. In particular the single D5 in Type IIB string theory will be seen to be related by T-duality to what has been described in the literature as the "magnetic" IIA brane configuration. We will then show how the D5 provides a strongly coupled, low energy description of weakly coupled IIA string theory in the original brane set up. We will start with a brane construction consisting of a number of Dirichlet fourbranes suspended between Dirichlet sixbranes in type IIA string theory on R 9 × S 1. The coordinate x 7 is compact, with radius R 7. In the classical approximation, the sixbranes are located at x 8 = x 9 = 0 and at some fixed x 6. The world volume coordinates for the sixbranes are x 0 , x 1 , x 2 , x 3 , x 4 , x 5 , x 7. The fourbranes are located at x 8 = x 9 = 0 and at some fixed values of x 4 , x 5 , x 7. The fourbranes have world volume coordinates x 0 , x 1 , x 2 , x 3 , x 6. Since the fourbranes stretch between the two sixbranes, the x 6 coordinate is restricted to a finite interval. This brane configuration is related to the configuration studied in [8] by T duality along x 1 , x 2 , x 3. The supersymmetries preserved by the fourbranes are of the form [9] ǫ L Q L + ǫ R Q R where ǫ L = Γ 0 Γ 1 Γ 2 Γ 3 Γ 6 ǫ R. Thus the fourbrane breaks one half of the supersymmetry. The sixbranes preserve supersymmetries of the form ǫ