2010

From weak to strong coupling in ABJM theory

Drukker, Nadav, Marino, Marcos, Putrov, Pavel

Understand

The partition function of N=6 supersymmetric Chern-Simons-matter theory (known as ABJM theory) on S^3, as well as certain Wilson loop observables, are captured by a zero dimensional super-matrix model.

This super-matrix model is closely related to a matrix model describing topological Chern-Simons theory on a lens space.
We explore further these recent observations and extract more exact results in ABJM theory from the matrix model.
In particular we calculate the planar free energy, which matches at strong coupling the classical IIA supergravity action on AdS_4 x CP^3 and gives the correct N^{3/2} scaling for the number of degrees of freedom of the M2 brane theory.

Built on

M. Mariño, R. Schiappa and M. Weiss, “Nonperturbative effects and the large-order behavior of matrix models and topological strings,” Commun. Number Theor. Phys. 2
Original
1954
Earlier work this paper cites.
I. Bars, “Supergroups and their representations,” Lectures Appl. Math. 21
Original
1983
Earlier work this paper cites.
E. Witten, “Quantum field theory and the Jones polynomial,” Commun. Math. Phys. 121
1989
Earlier work this paper cites.
E. Guadagnini, M. Martellini and M. Mintchev, “Wilson lines in Chern–Simons theory and link invariants,” Nucl. Phys. B 330
1990
Earlier work this paper cites.
S. H. Shenker, “The Strength of nonperturbative effects in string theory,” in O. Álvarez, E. Marinari and P. Windey (eds.), Random surfaces and quantum gravity,
1991
Earlier work this paper cites.
P. Candelas, X. C. De La Ossa, P. S. Green and L. Parkes, “A Pair of Calabi-Yau manifolds as an exactly soluble superconformal theory,” Nucl. Phys. B 359
1991
Earlier work this paper cites.
M. Alvarez and J. M. F. Labastida, “Analysis of observables in Chern–Simons perturbation theory,” Nucl. Phys. B 395
1993
Earlier work this paper cites.
M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, “Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes,” Commun. Math. Phys. 165
1994
Earlier work this paper cites.
N. Seiberg and E. Witten, “Electric-magnetic duality, monopole condensation, and confinement in 𝒩 = 2 {\cal N}=2 supersymmetric Yang-Mills theory,” Nucl. Phys. B 426
1994
Earlier work this paper cites.
J. Ambjorn, L. Chekhov, C. F. Kristjansen and Yu. Makeenko, “Matrix model calculations beyond the spherical limit,” Nucl. Phys. B 404
1995
Earlier work this paper cites.
I. R. Klebanov and A. A. Tseytlin, “Entropy of near-extremal black p-branes,” Nucl. Phys. B 475
1996
Earlier work this paper cites.
G. Akemann, “Higher genus correlators for the Hermitian matrix model with multiple cuts,” Nucl. Phys. B 482
1996
Earlier work this paper cites.
T. M. Chiang, A. Klemm, S. T. Yau and E. Zaslow, “Local mirror symmetry: Calculations and interpretations,” Adv. Theor. Math. Phys. 3
1999
Earlier work this paper cites.
V. Balasubramanian and P. Kraus, “A stress tensor for anti-de Sitter gravity,” Commun. Math. Phys. 208
1999
Earlier work this paper cites.
R. Emparan, C. V. Johnson and R. C. Myers, “Surface terms as counterterms in the AdS/CFT correspondence,” Phys. Rev. D 60
1999
Earlier work this paper cites.
J. K. Erickson, G. W. Semenoff and K. Zarembo, “Wilson loops in 𝒩 = 4 {\cal N}=4 supersymmetric Yang-Mills theory,” Nucl. Phys. B 582
2000
Earlier work this paper cites.
N. Drukker, D. J. Gross and A. A. Tseytlin, “Green-Schwarz string in AdS 5 × 𝕊 5 {}_{5}\times{\mathbb{S}}^{5} : Semiclassical partition function,” JHEP 0004
2000
Earlier work this paper cites.
N. Drukker and D. J. Gross, “An exact prediction of 𝒩 = 4 {\cal N}=4 SUSYM theory for string theory,” J. Math. Phys. 42
2001
Earlier work this paper cites.
K. Zarembo, “Supersymmetric Wilson loops,” Nucl. Phys. B 643
2002
Earlier work this paper cites.

Similar

A. Klemm, M. Mariño and S. Theisen, “Gravitational corrections in supersymmetric gauge theory and matrix models,” JHEP 0303
2003
Cited alongside, same era.
M. Mariño, “Chern–Simons theory, matrix integrals, and perturbative three-manifold invariants,” Commun. Math. Phys. 253
2004
Cited alongside, same era.
M. Aganagic, A. Klemm, M. Mariño and C. Vafa, “Matrix model as a mirror of Chern–Simons theory,” JHEP 0402
2004
Cited alongside, same era.
M. Tierz, “Soft matrix models and Chern–Simons partition functions,” Mod. Phys. Lett. A 19
2004
Cited alongside, same era.
H. Lin, O. Lunin and J. M. Maldacena, “Bubbling AdS space and 1 / 2 1/2 BPS geometries,” JHEP 0410
2004
Cited alongside, same era.
N. Drukker and B. Fiol, “All-genus calculation of Wilson loops using D-branes,” JHEP 0502
2005
Cited alongside, same era.
J. Gomis and F. Passerini, “Holographic Wilson loops,” JHEP 0608
2006
Cited alongside, same era.
N. Drukker, “1/4 BPS circular loops, unstable world-sheet instantons and the matrix model,” JHEP 0609
2006
Cited alongside, same era.
X. Arsiwalla, R. Boels, M. Mariño and A. Sinkovics, “Phase transitions in q-deformed 2d Yang-Mills theory and topological strings,” Phys. Rev. D 73
2006
Cited alongside, same era.
S. Yamaguchi, “Wilson loops of anti-symmetric representation and D5-branes,” JHEP 0605
2006
Cited alongside, same era.
S. A. Hartnoll and S. P. Kumar, “Higher rank Wilson loops from a matrix model,” JHEP 0608
2006
Cited alongside, same era.
Y. Dolivet and M. Tierz, “Chern–Simons matrix models and Stieltjes-Wigert polynomials,” J. Math. Phys. 48
2007
Cited alongside, same era.

Then

O. Aharony, O. Bergman and D. L. Jafferis, “Fractional M2-branes,” JHEP 0811
Original
2008
Later among the works it cites.
N. Drukker, J. Plefka and D. Young, “Wilson loops in 3-dimensional 𝒩 = 6 {\cal N}=6 supersymmetric Chern–Simons Theory and their string theory duals,” JHEP 0811
Original
2008
Later among the works it cites.
B. Haghighat, A. Klemm and M. Rauch, “Integrability of the holomorphic anomaly equations,” JHEP 0810
Original
2008
Later among the works it cites.
M. Aganagic, V. Bouchard and A. Klemm, “Topological strings and (almost) modular forms,” Commun. Math. Phys. 277
2008
Later among the works it cites.
M. Kruczenski and A. Tirziu, “Matching the circular Wilson loop with dual open string solution at 1-loop in strong coupling,” JHEP 0805
Original
2008
Later among the works it cites.
M. Mariño, “Open string amplitudes and large order behavior in topological string theory,” JHEP 0803
2008
Later among the works it cites.
A. Gustavsson, “Algebraic structures on parallel M2-branes,” Nucl. Phys. B 811
Original
2009
Later among the works it cites.
N. Halmagyi and V. Yasnov, “The spectral curve of the lens space matrix model,” JHEP 0911
2009
Later among the works it cites.
S. J. Rey, T. Suyama and S. Yamaguchi, “Wilson loops in superconformal Chern–Simons theory and fundamental strings in Anti-de Sitter supergravity dual,” JHEP 0903
Original
2009
Later among the works it cites.
N. Drukker, J. Gomis and D. Young, “Vortex Loop Operators, M2-branes and Holography,” JHEP 0903
Original
2009
Later among the works it cites.
O. Bergman and S. Hirano, “Anomalous radius shift in AdS 4 /CFT 3 ,” JHEP 0907
Original
2009
Later among the works it cites.
A. Kapustin and N. Saulina, “Chern–Simons-Rozansky-Witten topological field theory,” Nucl. Phys. B 823
Original
2009
Later among the works it cites.
A. Brini and A. Tanzini, “Exact results for topological strings on resolved Y ⁡ ( p , q ) Y(p,q) singularities,” Commun. Math. Phys. 289
Original
2009
Later among the works it cites.
V. Bouchard, A. Klemm, M. Mariño and S. Pasquetti, “Remodeling the B-model,” Commun. Math. Phys. 287
Original
2009
Later among the works it cites.
A. Kapustin, B. Willett and I. Yaakov, “Exact results for Wilson loops in superconformal Chern–Simons theories with matter,” JHEP 1003
Original
2010
Closest in time.
N. Drukker and D. Trancanelli, “A supermatrix model for 𝒩 = 6 {\cal N}=6 super Chern–Simons-matter theory,” JHEP 1002
Original
2010
Closest in time.
M. Mariño and P. Putrov, “Exact results in ABJM theory from topological strings,” JHEP 1006
Original
2010
Closest in time.
B. Chen and J. B. Wu, “Supersymmetric Wilson loops in 𝒩 = 6 {\cal N}=6 super Chern–Simons-matter theory,” Nucl. Phys. B 825
Original
2010
Closest in time.
A. Cagnazzo, D. Sorokin and L. Wulff, “String instanton in AdS 4 × ℂ ℙ 3 {}_{4}\times{\mathbb{C}}{\mathbb{P}}^{3} ,” JHEP 1005
Original
2010
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…