Duality of four dimensional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi mathvariant="script">N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:math> gauge theory

We show that the Seiberg-type duality of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi mathvariant="script">N</a:mi> <a:mo>=</a:mo> <a:mn>1</a:mn> </a:mrow> </a:math> gauge theory coupled with tensor chiral fields and fundamental chiral fields works if the meson spectrum built from the tensor fields takes a particular form: (a) It should be truncated. (b) The <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mi>R</d:mi> </d:math> charges of tensor fields <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mo stretchy="false">{</f:mo> <f:msub> <f:mi>R</f:mi> <f:mi>a</f:mi> </f:msub> <f:mo stretchy="false">}</f:mo> </f:math> and the truncated mesons <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mo stretchy="false">{</j:mo> <j:msub> <j:mi>R</j:mi> <j:mi>j</j:mi> </j:msub> <j:mo stretchy="false">}</j:mo> </j:math> take very special values. The meson spectrum so that the duality works is encoded elegantly in the factorization of the polynomial <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:msup> <n:mi>y</n:mi> <n:mi>n</n:mi> </n:msup> <n:mo>−</n:mo> <n:mn>1</n:mn> <n:mo>=</n:mo> <n:msub> <n:mi mathvariant="normal">Φ</n:mi> <n:mo>+</n:mo> </n:msub> <n:msub> <n:mi mathvariant="normal">Φ</n:mi> <n:mo>−</n:mo> </n:msub> </n:math> . Our consideration covers many known <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:mi mathvariant="script">N</r:mi> <r:mo>=</r:mo> <r:mn>1</r:mn> </r:math> dualities and generates a large class of new examples.