By Minxin Huang
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Extra resources for Aspects of supersymmetric guage theory and string theory
In weak coupling analysis the description in terms of non-interacting product gauge group factors is valid. More concretely, we can integrate out (in each gauge group factor) the massive adjoint chiral field, Φ, which has a mass well above Λ. The corresponding N = 1 theory thus obtained, valid below scales of order µ can be analyzed in various group factors separately. In each factor, it will become strongly coupled in the infra-red and will have vacua, details of which will depend on the number of flavors charged under the group factor.
Hence the breaking pattern is U(4) → U(1) × U(3). 3. Λ → 0, and a ∼ Λp with p > 1. 92). We find m1,2 ∼ ±ia and m3 ∼ − Λa 2 For m1,2 we get P4 (x) → x3 (x − 2Λ2 ), a which is a singular limit unless p = 2, in which case the gauge group breaks into U(4) → U(1) × U(3). For m3 we have P4 (x) → 2 x3 (x − Λa ), which is a singular limit unless p = 2, in which case the gauge group breaks into U(4) → U(1) × U(3). 48 Something interesting has happened here. To determine classical limits, we take a point on the factorization locus (parameterized by a and m) and then determine the superpotential which would yield that point as its minimum.
To make the above statement more clear, let us provide some calculations. First, according to our operation, the number of double index loops never increases whether under pasting or pinching. Second, we can calculate the total number of independent momentum loops ℓ by ℓ = P − V + 1 where P is the number of propagators and V , the number of vertices. 61) which means that the total number of momentum loops is just the sum of the individual ones. 62) which indicates the creation of one new momentum loop.