The line "Romance, now on the town, and Art, a vagrant" is from the poem "The Lonely Voice" by the poet Edwin Arlington Robinson. Robinson is known for his ability to capture the complexities of human emotion and the struggles of individual characters in a way that resonates with readers. His work often reflects themes of isolation and societal perception, which aligns with the sentiment expressed in this particular line. In this line, Robinson uses the imagery of "Romance" and "Art" as vagrants to highlight their transient nature in the context of society, suggesting that these concepts, while integral to the human experience, are often overlooked or marginalized. This reflects Robinson's broader themes of exploring the interplay between personal experience and societal values. The other poets listed—Robert Frost, William Wordsworth, and John Keats—each have distinct styles and thematic focuses that do not match the context of this line, making Robinson the fitting choice for this question.

Gwendolyn Brooks’s poetry often explores the complexities of social justice and urban life, particularly the experiences of African Americans in Chicago. Her work reflects on issues such as racial identity, community, and the struggles individuals face within urban settings. Brooks's ability to capture the essence of life in a city, coupled with her deep concern for social issues, resonates throughout her poetry, making this theme a central aspect of her writing. In her notable works, she frequently addresses the intersection of personal identity and broader societal challenges, illustrating how social injustices impact the lives of her characters. This focus on urban life and the quest for justice is particularly evident in her famous poem "We Real Cool," which presents the lives of young men navigating their identity in a challenging environment. The other themes, while present in various forms of literature, do not capture the essence of Brooks’s work as effectively. Nature and the environment, romantic love, and historical narratives are less prominent in her poetry compared to her poignant commentary on social justice and urban experiences.

Anna Akhmatova’s poetry is best characterized as lyric and emotional, a style that deeply reflects her personal experiences, feelings, and the tumultuous historical context in which she lived. Her work often conveys intense emotions, ranging from longing and love to despair and loss, making her poems resonate on a personal level with readers. Akhmatova’s use of vivid imagery and strong emotional currents illustrates a lyrical quality that elevates her writing beyond mere storytelling. This focus on personal and emotional themes aligns with the broader tradition of lyric poetry, where the expression of individual emotion is paramount. The other styles mentioned do reflect certain qualities of her work but do not encapsulate her overarching style as effectively. While her poetry does contain elements of symbolism and complexity, the primary impact of her writing lies in its ability to express deep emotion and personal reflection. Her approach does not typically lean towards free verse or experimental forms, which are distinct from the lyrical and emotional foundation that characterizes her most celebrated pieces.

The poem "Home Burial" is indeed written by Robert Frost; it was published in his collection "North of Boston" in 1914. This dramatic narrative explores the emotional distance between a husband and wife following the tragic death of their child. The intricate interplay of dialogue and vivid imagery captures the profound themes of grief, communication, and isolation. In contrast, the other options are associated with different poets. "The Waste Land" is a notable work by T.S. Eliot, renowned for its modernist themes and complex structure. "The Love Song of J. Alfred Prufrock," also by Eliot, is an early modernist poem that reflects the introspective thoughts of its protagonist. "Shantih shantih shantih," is a phrase from T.S. Eliot's "The Waste Land," specifically drawing from Sanskrit to convey a sense of peace as the poem closes. Each of these works is significant in its own right, but they do not belong to Robert Frost, which solidifies "Home Burial" as the accurate choice in this context.