Step 1: Concept Identification: The query seeks the regional theatre tradition for which Pammal Vijayaranga Sambandha Mudaliar is recognized as a foundational figure.
Step 2: Detailed Exposition: P. V. Sambandha Mudaliar (1873-1964) was a prominent figure in Indian theatre. A lawyer by profession, he devoted his life to theatrical reform and revitalization. He authored over 90 plays, adapted numerous Shakespearean works, and established the Suguna Vilasa Sabha, a theatre company that professionalized acting and production. Due to his significant contributions, he is widely regarded as the "Father of Modern Tamil Theatre".
Step 3: Conclusion: P. V. Sambandha Mudaliar is acknowledged as the father of Modern Tamil Theatre.