scholarly journals Subleading corrections to the S3 free energy of necklace quiver theories dual to massive IIA

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Junho Hong ◽  
James T. Liu
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Gauge Theories ◽  
Fermi Gas ◽  
Tree Level ◽  
Saddle Point Approximation ◽  
Higher Derivative ◽  
The Matrix ◽  
Hooft Limit ◽  
Chern Simons

Abstract We investigate the S3 free energy of $$ \mathcal{N} $$ N = 3 Chern-Simons-matter quiver gauge theories with gauge group U(N)r (r ≥ 2) where the sum of Chern-Simons levels does not vanish, beyond the leading order in the large-N limit. We take two different approaches to explore the sub-leading structures of the free energy. First we evaluate the matrix integral for the partition function in the ’t Hooft limit using a saddle point approximation. Second we use an ideal Fermi-gas model to compute the same partition function, but in the limit of fixed Chern-Simons levels. The resulting expressions for the free energy F = − log Z are then compared in the overlapping parameter regime. The Fermi-gas approach also hints at a universal $$ \frac{1}{6} $$ 1 6 log N correction to the free energy. Since the quiver gauge theories we consider are dual to massive Type IIA theory, we expect the sub-leading correction of the planar free energy in the large ’t Hooft parameter limit to match higher-derivative corrections to the tree-level holographic dual free energy, which have not yet been fully investigated.

Aharony–Bergman–Jafferis–Maldacena Wilson Loops in the Fermi Gas Approach

2013 ◽  
Vol 68 (1-2) ◽  
pp. 178-209 ◽  
Author(s):  
Albrecht Klemm ◽  
Marcos Mariño ◽  
Masoud Soroush
Keyword(s):  
Vacuum Expectation ◽  
Fermi Gas ◽  
Wilson Loops ◽  
Winding Number ◽  
Airy Functions ◽  
Mechanical Problem ◽  
Expectation Values ◽  
The Matrix ◽  
Statistical Mechanical ◽  
Chern Simons

The matrix model of the Aharony-Bergman-Jafferis-Maldacena theory can be formulated in terms of an ideal Fermi gas with a non-trivial one-particle Hamiltonian. We show that, in this formalism, vacuum expectation values (vevs) of Wilson loops correspond to averages of operators in the statistical-mechanical problem. This makes it possible to calculate these vevs at all orders in 1/N, up to exponentially small corrections, and for arbitrary Chern-Simons coupling, by using the Wentzel- Kramer-Brillouin expansion.We present explicit results for the vevs of 1/6 and the 1/2 Bogomolnyi- Prasad-Sommerfield Wilson loops, at any winding number, in terms of Airy functions. Our expressions are shown to reproduce the low genus results obtained previously in the ’t Hooft expansion.

scholarly journals UNAVOIDABLE CONFLICT BETWEEN MASSIVE GRAVITY MODELS AND MASSIVE TOPOLOGICAL TERMS

2004 ◽  
Vol 19 (11) ◽  
pp. 817-826 ◽  
Author(s):  
ANTONIO ACCIOLY ◽  
MARCO DIAS
Keyword(s):  
Three Dimensional ◽  
Massive Gravity ◽  
Ricci Scalar ◽  
Gravity Models ◽  
Tree Level ◽  
Common Belief ◽  
Higher Derivative ◽  
The Common ◽  
Chern Simons ◽  
Topological Term

Massive gravity models in (2+1) dimensions, such as those obtained by adding to Einstein's gravity the usual Fierz–Pauli, or the more complicated Ricci scalar squared (R2), terms, are tree level unitary. Interesting enough these seemingly harmless systems have their unitarity spoiled when they are augmented by a Chern–Simons term. Furthermore, if the massive topological term is added to [Formula: see text] gravity, or to [Formula: see text] gravity (higher-derivative gravity), which are nonunitary at the tree level, the resulting models remain nonunitary. Therefore, unlike the common belief, as well as the claims in the literature, the coexistence between three-dimensional massive gravity models and massive topological terms is conflicting.

scholarly journals Subleading corrections to the free energy in a theory with N5/3 scaling

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
James T. Liu ◽  
Yifan Lu
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Gauge Group ◽  
Leading Order ◽  
Numerical Evidence ◽  
Matter Theory ◽  
Chern Simons

Abstract We numerically investigate the sphere partition function of a Chern-Simons-matter theory with SU(N) gauge group at level k coupled to three adjoint chiral multiplets that is dual to massive IIA theory. Beyond the leading order N5/3 behavior of the free energy, we find numerical evidence for a term of the form (2/9) log N. We conjecture that this term may be universal in theories with N5/3 scaling in the large-N limit with the Chern-Simons level k held fixed.

scholarly journals NUMERICAL STUDIES OF THE ABJM THEORY FOR ARBITRARY N AT ARBITRARY COUPLING CONSTANT

2013 ◽  
Vol 21 ◽  
pp. 203-205
Author(s):  
MASAZUMI HONDA ◽  
MASANORI HANADA ◽  
YOSHINORI HONMA ◽  
JUN NISHIMURA ◽  
SHOTARO SHIBA ◽  
...  
Keyword(s):  
Fermi Gas ◽  
Coupling Constant ◽  
Abjm Theory ◽  
Localization Method ◽  
Arbitrary Coupling ◽  
Numerical Studies ◽  
Matter Theory ◽  
The Matrix ◽  
Genus Expansion ◽  
Chern Simons

We show that the ABJM theory, which is an [Formula: see text] superconformal U (N) × U (N) Chern-Simons matter theory, can be studied for arbitrary N at arbitrary coupling constant by applying a simple Monte Carlo method to the matrix model derived by using the localization method. Here we calculate the free energy, and show that some results obtained by the Fermi gas approach can be clearly understood from the constant map contribution obtained by the genus expansion.

scholarly journals The L∞ structure of gauge theories with matter

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Humberto Gomez ◽  
Renann Lipinski Jusinskas ◽  
Cristhiam Lopez-Arcos ◽  
Alexander Quintero Vélez
Keyword(s):  
Perturbation Theory ◽  
Scattering Amplitudes ◽  
Quantum Chromodynamics ◽  
Minimal Model ◽  
Gauge Theories ◽  
Algebraic Approach ◽  
Field Theories ◽  
Tree Level ◽  
Scalar Quantum ◽  
Chern Simons

Abstract In this work we present an algebraic approach to the dynamics and perturbation theory at tree-level for gauge theories coupled to matter. The field theories we will consider are: Chern-Simons-Matter, Quantum Chromodynamics, and scalar Quantum Chromodynamics. Starting with the construction of the master action in the classical Batalin-Vilkovisky formalism, we will extract the L∞-algebra that allow us to recursively calculate the perturbiner expansion from its minimal model. The Maurer-Cartan action obtained in this procedure will then motivate a generating function for all the tree-level scattering amplitudes. There are two interesting outcomes of this construction: a generator for fully-flavoured amplitudes via a localisation on Dyck words; and closed expressions for fermion and scalar lines attached to n-gluons with arbitrary polarisations.

scholarly journals More on topological vertex formalism for 5-brane webs with O5-plane

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Hirotaka Hayashi ◽  
Rui-Dong Zhu
Keyword(s):  
Gauge Theory ◽  
Partition Function ◽  
Vertex Operator ◽  
Vertex Function ◽  
Gauge Theories ◽  
Partition Functions ◽  
Topological Vertex ◽  
Concrete Form ◽  
Nekrasov Partition Functions ◽  
Chern Simons

Abstract We propose a concrete form of a vertex function, which we call O-vertex, for the intersection between an O5-plane and a 5-brane in the topological vertex formalism, as an extension of the work of [1]. Using the O-vertex it is possible to compute the Nekrasov partition functions of 5d theories realized on any 5-brane web diagrams with O5-planes. We apply our proposal to 5-brane webs with an O5-plane and compute the partition functions of pure SO(N) gauge theories and the pure G2 gauge theory. The obtained results agree with the results known in the literature. We also compute the partition function of the pure SU(3) gauge theory with the Chern-Simons level 9. At the end we rewrite the O-vertex in a form of a vertex operator.

VIRASORO CONSTRAINTS ON THE MATRIX-MODEL PARTITION FUNCTION AND STRING FIELD THEORY

1992 ◽  
Vol 07 (07) ◽  
pp. 1553-1581 ◽  
Author(s):  
ASHOKE SEN
Keyword(s):  
Field Theory ◽  
Partition Function ◽  
Matrix Model ◽  
String Field Theory ◽  
Minimal Model ◽  
Differential Operators ◽  
Tree Level ◽  
Virasoro Constraints ◽  
The Matrix ◽  
The One

The one-matrix model at the kth multicritical point is known to describe the (2, 2k–1) minimal model coupled to gravity, and the partition function of this model is known to obey a set of Virasoro constraints generated by a set of differential operators Ln. Working at the tree level of string theory, and using the Feigin-Fuchs description of the (2, 2k–1) minimal model, we show that the Virasoro constraints generated by Li (0≤i≤k−2) can be identified with a set of gauge symmetries of the corresponding string field theory.

scholarly journals Integrability of type 0A matrix model in the presence of D-brane

2019 ◽  
Vol 34 (03n04) ◽  
pp. 1950020
Author(s):  
Chandrima Paul
Keyword(s):  
Free Energy ◽  
String Theory ◽  
Partition Function ◽  
Matrix Model ◽  
Canonical Ensemble ◽  
Fredholm Determinant ◽  
Grand Canonical Ensemble ◽  
Integrable Structure ◽  
The Matrix ◽  
Grand Canonical

We consider type 0A matrix model in the presence of spacelike D-brane which is localized in matter direction at any arbitrary point. In string theory, the boundary state, which in matrix model corresponds to the Laplace transform of the macroscopic loop operator, is known to obey the operator constraints corresponding to open string boundary condition. When we analyze MQM as well as the respective collective field theory and compare it with dual string theory, it appears that consistency of the theory requires a condition equivalent to a constraint on the matter part that needed to be imposed in the matrix model. We identified this condition and observed that this results in constraining the macroscopic loop operator so that it projects the Hilbert space generated by the operator to its physical sector at the point of insertion while keeping the bulk matrix model unaffected, thereby describing a situation parallel to string theory. We analyzed the theory with uncompactified time and have shown explicitly that the matrix model predictions are in good agreement with the relevant string theory. Next, we considered the theory with compactified time, analyzed MQM on a circle in the presence of D-brane. We evaluated the partition function along with the constrained macroscopic loop operator in the grand canonical ensemble and showed the free energy corresponds to that of a deformed Fermi surface. We have also shown that the path integral in the presence of D-brane can be expressed as the Fredholm determinant. We have studied the fermionic scattering in a semiclassical regime. Finally, we considered the compactified theory in the presence of the D-brane with tachyonic background. We evaluated the free energy in the grand canonical ensemble. We have shown the integrable structure of the respective partition function and it corresponds to the tau function of Toda hierarchy. We have also analyzed the dispersionless limit.

scholarly journals The large-N partition function for non-parity-invariant Chern-Simons-matter theories

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
James T. Liu ◽  
Xiuyuan Zhang
Keyword(s):  
Partition Function ◽  
Airy Function ◽  
Fermi Gas ◽  
Large N ◽  
Chern Simons

Abstract We extend the Fermi gas approach to a class of ABJM-like necklace quiver theories without parity invariance. The resulting partition function on S3 retains the form of an Airy function, but now includes a phase that scales as Nk in the large-N limit where k is an overall Chern-Simons level. We demonstrate the presence of this phase both analytically and numerically in the case of a three node quiver.

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