Reading between the lines of four-dimensional gauge theories
By O. Aharony, N. Seiberg, Yuji Tachikawa. 2013
480 citations recorded by the source corpus.
A bstractStarting with a choice of a gauge group in four dimensions, there is often freedom in the choice of magnetic and dyonic line operators. Different consistent choices of these operators correspond to distinct physical theories, with the same correlation functions of local operators in $ {{\mathbb{R}}^4} $. In some cases these choices are permuted by shifting the θ-angle by 2π. In other cases they are labeled by new discrete θ-like parameters. Using this understanding we gain new insight into the dynamics of four-dimensional gauge theories and their phases. The existence of these distinct theories clarifies a number of issues in electric/magnetic dualities of supersymmetric gauge theories, both for the conformal $ \mathcal{N} $ = 4 theories and for the low-energy dualities of $ \mathcal{N} $ = 1 theories.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/d675ec703612fbf399d877e79cfa5e75d9556ed7
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Astronomy and Astrophysics
In Nuclear and High Energy Physics
Citations in the corpus
- TASI Lectures on the Conformal Bootstrap (2016, background): “Also, 4d conformal gauge theories admit different sets of line operators for the same set of local operators [42].”
- On the Defect Group of a 6D SCFT (2015, background): “For example, in the context of four-dimensional theories, the spectrum of line operators and surface operators must be specified [1–6].”
- Anomalies in the space of coupling constants and their dynamical applications II (2019, unknown): “6 of [44] for N “ 6 mod 8.”
- Notes on generalized global symmetries in QFT (2015, methodology): “This was the strategy followed in [53, 54] to distinguish SU(2) from SO(3) theories, for example.”
- Comments on global symmetries, anomalies, and duality in (2 + 1)d (2017, methodology): “(for more details see [60] and references therein).”
- Comments on twisted indices in 3d supersymmetric gauge theories (2016, background): “57) (7)Note that a Wilson loop is defined in terms of a representation R of the gauge group G instead of the algebra g, although we will not discuss any of the interesting subtleties associated to this fact — see for instance [51, 61].”
- The geometry of supersymmetric partition functions (2013, unknown): “See [17] for a recent example.”
- Comments on one-form global symmetries and their gauging in 3d and 4d (2018, background): “he Witten eect it acquires electric charge kas is shifted by 2ˇk. Then we restore the original and have nonzero p= k(N 1). This means that the basic line operator has electric charge p, i.e. it is [10] Tb( p) = T( )W( ) : (4.13) Note that this is a genuine line operator, which does not need a surfac”
- Theta, time reversal and temperature (2017, methodology): “We use the notation of [24] and organize line operators into families labeled by pairs (a, b) ∈ ZN × ZN .”
- Localization techniques in quantum field theories (2016, methodology): “This means that, unlike the S3 b partition function, the lens space partition function is sensitive to issues related to the global structure of the gauge group [33].”
- Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions (2022, methodology): “Similarly, gauging the Z((1)) 2 subgroup one-form symmetry given by the first Z((1)) 2 in the Z (1) 2 × Z((1)) 2 center one-form symmetry gives the Sc(8) gauge theory, 27The discrete theta angles for Spin(4n)/(Z2×Z2) bundle can be specified by n11, n22, n12 that take value in Z2 on spin manifolds, w”
- Generalized global symmetries (2014, background): “There are two different 4d theories with gauge group SO(2n), which differ by a discrete θ-parameter [15].”
- Symmetries in Quantum Field Theory and Quantum Gravity (2018, background): “But does this then mean that if G and G′ have the same Lie Algebra, then pure Yang-Mills theory on R with gauge group G is identical to pure Yang-Mills theory on R with gauge group G′? This question was studied in detail in [125], where it was argued that in fact they are different.”
- Deconfined quantum critical points: symmetries and dualities (2017, background): “[44], which distinguishes it from a trivial gapped phase of SO(5)symmetric bosons.”
- N=2 Supersymmetric Dynamics for Pedestrians (2013, methodology): “The idea is to use the behavior of the potential between two external particles which are magnetically or dyonically charged as the order parameter [49].”